tag:blogger.com,1999:blog-52401725965011494962024-03-13T11:40:32.425-07:00วิชา คณิตศาสตร์ เรื่อง เมทริกซ์Anonymoushttp://www.blogger.com/profile/13820467283799737113noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5240172596501149496.post-78433180531241872942012-09-22T21:38:00.000-07:002012-09-26T23:17:07.895-07:00<a href="http://2.bp.blogspot.com/-Bplh6yKLmxo/UGClRwvmL6I/AAAAAAAAAJo/4DuwPzv8T48/s1600/p3.gif" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-Bplh6yKLmxo/UGClRwvmL6I/AAAAAAAAAJo/4DuwPzv8T48/s1600/p3.gif" /></a><a href="http://1.bp.blogspot.com/-Ea-1JfNKANk/UGCkDoJ4ZZI/AAAAAAAAAIE/KzWAtdCM8bY/s1600/1191691195.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-Ea-1JfNKANk/UGCkDoJ4ZZI/AAAAAAAAAIE/KzWAtdCM8bY/s1600/1191691195.gif" /></a><br />
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<span style="font-size: x-large;"><b style="color: #274e13; font-family: Times, 'Times New Roman', serif;"> </b><span style="color: #274e13; font-family: Times, 'Times New Roman', serif; text-align: left;">เมท</span><span style="color: #274e13; font-family: Times, 'Times New Roman', serif; text-align: left;">ริกซ์ </span></span></div>
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<b><span style="color: purple;"><span style="font-family: Verdana, sans-serif;"> ในคณิตศาสตร์ เมทริกซ์ หรือ เมตริกซ์ (อังกฤษ: <span lang="en" style="background-image: none;" xml:lang="en">matrix</span>) คือตารางสี่เหลี่ยมที่แต่ละช่องบรรจุจำนวนหรือโครงสร้างทางคณิตศาสตร์ที่สามารถนำมาบวกและคูณกับตัวเลขได้</span></span></b></div>
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<b><span style="color: purple; font-family: Verdana, sans-serif;"> เราสามารถใช้เมทริกซ์แทนระบบสมการเชิงเส้น การแปลงเชิงเส้น และใช้เก็บข้อมูลที่ขึ้นกับตัวแปรต้นสองตัว เราสามารถบวก คูณ และแยกเมทริกซ์ออกเป็นผลคูณของเมทริกซ์ได้หลายรูปแบบ เมทริกซ์เป็นแนวความคิดที่มีความสำคัญยิ่งของพีชคณิตเชิงเส้น โดยทฤษฎีเมทริกซ์เป็นสาขาหนึ่งของพีชคณิตเชิงเส้นที่เน้นการศึกษาเมทริกซ์</span></b></div>
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<b style="text-align: start;"><b><span style="color: #a64d79;">ในบทความนี้ แต่ละช่องของเมทริกซ์จะบรรจุจำนวนจริงหรือจำนวนเชิงซ้อน หากไม่ได้ระบุเป็นอย่างอื่น</span></b></b></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><u><span style="color: #006666;">1. นิยามของเมท</span></u><u><span style="color: #006666;">ริกซ์</span></u></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><u><span style="color: maroon;">นิยามที่ 1</span></u><span style="color: maroon;"> เมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">คือ กลุ่มของจำนวนจริง หรือ </span></span></div>
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<span style="color: maroon;"><span style="font-family: Arial, Helvetica, sans-serif;">จำนวนเชิงซ้อน
มาจัดเรียงเป็นรูปสี่เหลี่ยมผืนผ้าเป็น</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: maroon;">แถวตามแนวนอน </span><span style="color: maroon;">(Horizontal) </span><span style="color: maroon;">และ แนวตั้ง </span><span style="color: maroon;">(Vertical)</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: maroon;">ซึ่งมีแถวตามแนวนอนเรียกว่า </span><span style="color: #006666; font-style: italic;">แถว </span><span style="color: #006666; font-style: italic;">(Row)</span><span style="color: maroon;"> </span><span style="color: maroon;">และตาม</span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: maroon;">แนวตั้งเรียกว่า </span><span style="color: #006666; font-style: italic;">หลัก </span><span style="color: #006666; font-style: italic;">(Column)</span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #006666; font-style: italic;">เมท</span><span style="color: #006666; font-style: italic;">ริกซ์</span><span style="color: #006666; font-style: italic;">ศูนย์ </span><span style="color: #006666; font-style: italic;">(Zero
Matrix</span><span style="color: #006666; font-style: italic;">
</span><span style="color: maroon;">หรือ</span><span style="color: #006666; font-style: italic;"> </span><span style="color: #006666; font-style: italic;">Null
Matrix)</span></span></div>
<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: maroon;">คือ เมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">ที่มีสมาชิกทุกตัวเป็นศูนย์หมด </span></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #006666; font-style: italic;">เมท</span><span style="color: #006666; font-style: italic;">ริกซ์</span><span style="color: #006666; font-style: italic;">ทแยงมุม</span><span style="color: #006666; font-style: italic;">(Diagonal
Matrix)</span><span style="color: maroon;"> </span><span style="color: maroon;">คือเมท</span><span style="color: maroon;">ริกซ์</span></span></div>
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<span style="color: maroon;"><span style="font-family: Georgia, Times New Roman, serif;">จัตุรัสที่มีสมาชิกทุกตัวที่ไม่ได้อยู่บนเส้นทแยงมุมหลัก</span></span></div>
<span style="color: maroon;"><span style="font-family: Georgia, Times New Roman, serif;">มีค่าเป็นศูนย์ทั้งหมด </span></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #006666; font-style: italic;">เมท</span><span style="color: #006666; font-style: italic;">ริกซ์เชิงส</span><span style="color: #006666; font-style: italic;">เก</span><span style="color: #006666; font-style: italic;">ล่าร์</span><span style="color: #006666; font-style: italic;">(Scalar
Matrix)</span><span style="color: maroon;"> </span><span style="color: maroon;">คือเมท</span><span style="color: maroon;">ริกซ์</span></span></div>
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<span style="color: maroon;"><span style="font-family: Georgia, Times New Roman, serif;">ทแยงมุมที่มีสมาชิกทุกตัวบนเส้นทแยงมุมหลักมีค่าเท่ากัน</span></span></div>
<span style="color: maroon;"><span style="font-family: Georgia, Times New Roman, serif;">ทั้งหมด </span></span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #006666; font-style: italic;">เมท</span><span style="color: #006666; font-style: italic;">ริกซ์</span><span style="color: #006666; font-style: italic;">เอกลักษณ์ </span><span style="color: #006666; font-style: italic;">(Identity
Matrix </span><span style="color: maroon; font-style: italic;">หรือ</span><span style="color: #006666; font-style: italic;"> </span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #006666; font-style: italic;">Unit
Matrix)</span><span style="color: maroon;"> </span><span style="color: maroon;">คือ เมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">ทแยงมุมที่มีสมาชิกทุกตัวบน</span></span></div>
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<span style="color: maroon;"><span style="font-family: Georgia, Times New Roman, serif;">เส้นทแยงมุมหลักมีค่าเท่ากับ 1 ทั้งหมด
ใช้สัญลักษณ์ </span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #006666; font-style: italic;">I</span><span style="color: maroon;"> </span><span style="color: maroon;">หรือ
</span><span style="color: #006666; font-style: italic;">I</span><span style="color: #006666; font-style: italic; vertical-align: sub;">n</span><span style="color: maroon;"> </span><span style="color: maroon;">แทนเอกลักษณ์เมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">อันดับ
</span><span style="color: maroon; font-style: italic;">n</span></span><span style="color: maroon; font-family: 'Angsana New'; font-size: 40pt;"> </span><br />
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<span style="font-family: Georgia, Times New Roman, serif;"><u><span style="color: #006666; font-style: italic;">3.
ชนิดของเมท</span></u><u><span style="color: #006666; font-style: italic;">ริกซ์</span></u></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #006666; font-style: italic;">3.1 เมท</span><span style="color: #006666; font-style: italic;">ริกซ์</span><span style="color: #006666; font-style: italic;">สลับเปลี่ยน </span><span style="color: #006666; font-style: italic;">(Transposed
Matrix)</span></span></div>
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<span style="color: #006666; font-family: Georgia, Times New Roman, serif;"><i> </i></span><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px;">ถ้า</span><span style="color: #006666; font-family: Georgia, Times New Roman, serif;"><i> </i></span><a href="http://4.bp.blogspot.com/-Xxy__PoDNT4/UGCdfItXY-I/AAAAAAAAAF4/WL8y2epcwjg/s1600/%25E0%25B8%25A3%25E0%25B8%25B9%25E0%25B8%259B%25E0%25B8%25A0%25E0%25B8%25B2%25E0%25B8%259E7.png" imageanchor="1" style="color: #444444; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="67" src="http://4.bp.blogspot.com/-Xxy__PoDNT4/UGCdfItXY-I/AAAAAAAAAF4/WL8y2epcwjg/s200/%25E0%25B8%25A3%25E0%25B8%25B9%25E0%25B8%259B%25E0%25B8%25A0%25E0%25B8%25B2%25E0%25B8%259E7.png" width="200" /></a><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px;">แล้ว เมท</span><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px;">ริกซ์</span><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px;">สลับเปลี่ยนของ </span><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; font-style: italic; line-height: 20px;">A</span></div>
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<span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px; text-align: left;"> </span><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px; text-align: left;">คือ </span><a href="http://4.bp.blogspot.com/-CoFS6yEOizE/UGCfCPu8d8I/AAAAAAAAAGA/-Y9M6yT_2OI/s1600/%E0%B8%A3%E0%B8%B9%E0%B8%9B%E0%B8%A0%E0%B8%B2%E0%B8%9E9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="69" src="http://4.bp.blogspot.com/-CoFS6yEOizE/UGCfCPu8d8I/AAAAAAAAAGA/-Y9M6yT_2OI/s200/%E0%B8%A3%E0%B8%B9%E0%B8%9B%E0%B8%A0%E0%B8%B2%E0%B8%9E9.png" width="200" /></a><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px; text-align: left;">และใช้สัญลักษณ์ </span><span style="color: #006666; font-family: Georgia, 'Times New Roman', serif; font-style: italic; line-height: 20px; text-align: left;">A</span><span style="color: #006666; font-family: Georgia, 'Times New Roman', serif; font-style: italic; line-height: 20px; text-align: left; vertical-align: super;">T</span><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px; text-align: left;"> </span><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px; text-align: left;">หรือ </span><span style="color: maroon; font-family: Georgia, 'Times New Roman', serif; line-height: 20px; text-align: left;"> </span><span style="color: #006666; font-family: Georgia, 'Times New Roman', serif; font-style: italic; line-height: 20px; text-align: left;">A'</span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: maroon;">
</span><span style="color: maroon;">แทนเมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">สลับเปลี่ยนของ
</span><span style="color: maroon;"> </span><span style="color: maroon; font-style: italic;">A</span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: #006666; font-style: italic;">3.4 เมท</span><span style="color: #006666; font-style: italic;">ริกซ์</span><span style="color: #006666; font-style: italic;">สามเหลี่ยม </span><span style="color: #006666; font-style: italic;">(Triangular
Matrix)</span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: maroon;">เมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">สามเหลี่ยมบน </span><span style="color: #006666; font-style: italic;">(Lower Triangular Matrix)</span><span style="color: maroon;"> คือ </span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: maroon;">เมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">จัตุรัสใดๆ
ที่มีสมาชิกทุกตัวที่อยู่เหนือเส้นทแยงมุมหลัก</span></span></div>
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<span style="color: maroon;"><span style="font-family: Georgia, Times New Roman, serif;">เป็นศูนย์หมด </span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: maroon;">เมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">สามเหลี่ยมล่าง </span><span style="color: #006666; font-style: italic;">(Upper Triangular Matrix)</span><span style="color: maroon;"> คือ </span></span></div>
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<span style="font-family: Georgia, Times New Roman, serif;"><span style="color: maroon;">เมท</span><span style="color: maroon;">ริกซ์</span><span style="color: maroon;">จัตุรัสใดๆ
ที่มีสมาชิกทุกตัวที่อยู่ใต้เส้นทแยงมุมหลัก</span></span></div>
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<span style="color: maroon;"><span style="font-family: Georgia, Times New Roman, serif;">เป็นศูนย์หมด </span></span></div>
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<span style="color: blue; font-family: Arial, Helvetica, sans-serif; font-size: large;">ดีเทอร์มิแนนต์ของเมทริกซ์</span></div>
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<span style="color: #38761d;"><span style="font-family: Georgia, Times New Roman, serif;"> </span><span style="font-family: Arial, Helvetica, sans-serif;"> ดีเทอร์มิแนนต์ของเมทริกซ์
det(A) มีความสำคัญใน</span></span><br />
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<span style="color: #38761d; font-family: Arial, Helvetica, sans-serif; line-height: 80%; text-indent: -0.38in;">การ</span><span style="color: #38761d; font-family: Arial, Helvetica, sans-serif; line-height: 80%; text-indent: -0.38in;">คำนวณทางคณิตศาสตร์ วิธีคำนวณหาดีเทอร์มิแนนต์มีหลาย </span><br />
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<span style="color: #38761d; font-family: Arial, Helvetica, sans-serif; line-height: 80%; text-indent: -0.38in;">วิธีดังนี้</span><span style="color: #38761d; font-family: Arial, Helvetica, sans-serif; line-height: 80%; text-indent: -0.38in;">การหาโดยตรง
(ในกรณีของเมทริกซ์ขนาดเล็ก)
เช่น</span></div>
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<span style="color: magenta; font-family: Georgia, Times New Roman, serif;"><span style="font-weight: normal;">เมท</span><span style="font-weight: normal;">ริกซ์</span><span style="font-weight: normal;">ขนาด
</span><span style="font-weight: normal;">2x2</span><span style="font-weight: normal;"> (หาดี</span><span style="font-weight: normal;">เทอร์มิแนนต์</span><span style="font-weight: normal;">ได้ในกรณีของเมท</span><span style="font-weight: normal;">ริกซ์จตุรัส</span><span style="font-weight: normal;">เท่านั้น)</span></span><br />
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<span style="color: magenta; font-family: Georgia, Times New Roman, serif;"><span style="font-weight: normal;">เมท</span><span style="font-weight: normal;">ริกซ์</span><span style="font-weight: normal;">ขนาด
</span><span style="font-weight: normal;">3x3</span></span><span style="color: #2f1311; font-family: 'Angsana New'; font-size: 32pt; font-weight: normal;">
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<span style="color: red; font-family: Georgia, Times New Roman, serif;"><span style="font-weight: normal;">เมท</span><span style="font-weight: normal;">ริกซ์</span><span style="font-weight: normal;">ที่มีขนาดมากกว่านี้จะทำแบบนี้ไม่ได้
ต้องใช้วิธีกระจาย </span><span style="font-weight: normal;">cofactor </span><span style="font-weight: normal;">เท่านั้น</span></span></div>
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<span style="color: blue; font-family: Arial, Helvetica, sans-serif; font-size: large;">การหาคำตอบของระบบสมการเชิงเส้นด้วยเมทริกซ์</span><span style="color: #f7d47d; font-family: 'Angsana New'; font-size: 28pt;">
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<span style="font-weight: normal;"><span style="color: purple; font-family: Georgia, Times New Roman, serif;"> วิธีการหาคำตอบของระบบสมการเชิงเส้นมี
3 วิธีคือ</span></span></div>
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<span style="color: purple; font-family: Georgia, Times New Roman, serif;"><span style="font-weight: normal;"> 1 </span><span style="font-weight: normal;">ใช้
</span><span style="font-weight: normal;">Inverse matrix</span><span style="font-weight: normal;">
เหมาะกับระบบที่มีสมการจำนวนไม่มาก (2-3 สมการ)</span></span></div>
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<span style="color: purple; font-family: Georgia, Times New Roman, serif;"><span style="font-weight: normal;"> 2 </span><span style="font-weight: normal;">ใช้
</span><span style="font-weight: normal;">Cramer’s rule</span><span style="font-weight: normal;">
เหมาะกับระบบที่มีสมการจำนวนไม่มาก</span></span></div>
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<span style="color: purple; font-family: Georgia, Times New Roman, serif;"><span style="font-weight: normal;"> </span><span style="font-weight: normal;">3
</span><span style="font-weight: normal;">ใช้วิธีการของ </span><span style="font-weight: normal;">Gauss-Elimination</span><span style="font-weight: normal;">
ซึ่งเหมาะกับระบบที่มีสมการจำนวนมาก</span></span></div>
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<b>เพิ่มเติม </b></div>
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<b><a href="http://www.tewlek.com/anet_matrix.html" target="_blank">สรุป เนื้อหาสำคัญ</a></b><br />
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<span class="long-title " dir="ltr" id="eow-title" style="background-color: transparent; background-position: initial initial; background-repeat: initial initial; border: 0px; font-size: 0.9166em; letter-spacing: -0.5px; margin: 0px; padding: 0px;" title="Tutor Channel เมทริกซ์ พี่เอ๋ Part 1"><a href="http://tutor%20channel%20%E0%B9%80%E0%B8%A1%E0%B8%97%E0%B8%A3%E0%B8%B4%E0%B8%81%E0%B8%8B%E0%B9%8C%20%E0%B8%9E%E0%B8%B5%E0%B9%88%E0%B9%80%E0%B8%AD%E0%B9%8B%20part%201/" target="_blank">Tutor Channel เมทริกซ์ พี่เอ๋ Part 1</a></span></h1>
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<h1 id="watch-headline-title" style="background-color: #ebebeb; border: 0px; color: #333333; font-family: arial, sans-serif; font-size: 1.8333em; height: 1.1363em; line-height: 1.1363em; margin: 0px 0px 5px; max-height: 1.1363em; overflow: hidden; padding: 0px; text-align: start;">
<span class="long-title " dir="ltr" id="eow-title" style="background-color: transparent; background-position: initial initial; background-repeat: initial initial; border: 0px; font-size: 0.9166em; letter-spacing: -0.5px; margin: 0px; padding: 0px;" title="Tutor Channel เมทริกซ์ พี่เอ๋ Part 2"><a href="http://www.youtube.com/watch?v=_dqTptS5rts&feature=relmfu" target="_blank">Tutor Channel เมทริกซ์ พี่เอ๋ Part 2</a></span></h1>
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<span class="long-title " dir="ltr" id="eow-title" style="background-color: transparent; background-position: initial initial; background-repeat: initial initial; border: 0px; font-size: 0.9166em; letter-spacing: -0.5px; margin: 0px; padding: 0px;" title="Matrix เมตริกซ์ ม.4 [1/4] By www.tutoroui.com"><a href="http://www.youtube.com/watch?v=VHXml7A78Do&feature=related" target="_blank">Matrix เมตริกซ์ ม.4 [1/4] By www.tutoroui.com</a></span></h1>
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<span class="long-title " dir="ltr" id="eow-title" style="background-color: transparent; background-position: initial initial; background-repeat: initial initial; border: 0px; font-size: 0.9166em; letter-spacing: -0.5px; margin: 0px; padding: 0px;" title="Matrix เมตริกซ์ ม.4 [2-4] By www.tutoroui.com"><a href="http://www.youtube.com/watch?v=UKsHZivHKJ8&feature=relmfu" target="_blank">Matrix เมตริกซ์ ม.4 [2-4] By www.tutoroui.com</a></span></h1>
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<h1 id="watch-headline-title" style="background-color: #ebebeb; border: 0px; color: #333333; font-family: arial, sans-serif; font-size: 1.8333em; height: 1.1363em; line-height: 1.1363em; margin: 0px 0px 5px; max-height: 1.1363em; overflow: hidden; padding: 0px; text-align: start;">
<span class="long-title " dir="ltr" id="eow-title" style="background-color: transparent; background-position: initial initial; background-repeat: initial initial; border: 0px; font-size: 0.9166em; letter-spacing: -0.5px; margin: 0px; padding: 0px;" title="Matrix เมตริกซ์ ม.4 [3-4] By www.tutoroui.com"><a href="http://www.youtube.com/watch?v=9_6hfMSu9uw&feature=relmfu" target="_blank">Matrix เมตริกซ์ ม.4 [3-4] By www.tutoroui.com</a></span></h1>
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<h1 id="watch-headline-title" style="background-color: #ebebeb; border: 0px; color: #333333; font-family: arial, sans-serif; font-size: 1.8333em; height: 1.1363em; line-height: 1.1363em; margin: 0px 0px 5px; max-height: 1.1363em; overflow: hidden; padding: 0px; text-align: start;">
<span class="long-title " dir="ltr" id="eow-title" style="background-color: transparent; background-position: initial initial; background-repeat: initial initial; border: 0px; font-size: 0.9166em; letter-spacing: -0.5px; margin: 0px; padding: 0px;" title="Matrix เมตริกซ์ ม.4 [4-4] By www.tutoroui.com"><a href="http://www.youtube.com/watch?v=tWXHwSAeS-I&feature=relmfu" target="_blank">Matrix เมตริกซ์ ม.4 [4-4] By www.tutoroui.com</a></span></h1>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">แบบทดสอบ</span></b><br />
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<b><br /></b><b><a href="http://www.igetweb.com/www/cicschool/private_folder/test/metrix.pdf" target="_blank">แบบทดสอบ เรื่อง เมทริกซ์</a></b></div>
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<b><a href="http://www.igetweb.com/www/cicschool/private_folder/test/metrix_ans1.pdf" target="_blank">เฉลยแบบทดสอบ เรื่อง เมทริกซ์ ตอนที่ 1</a></b></div>
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<b><a href="http://www.igetweb.com/www/cicschool/private_folder/test/metrix_ans2.pdf" target="_blank">เฉลยแบบทดสอบ เรื่อง เมทริกซ์ ตอนที่ 2</a></b><br />
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<b> บทความนี้สำเร็จได้ต้องขอขอบคุณ Youtube และพี่ๆติวเตอร์ ที่นำคลิปวิดิโอมาลงเผยแพร่ </b></div>
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<b> บทความนี้เป็นส่วนหนึ่งของรายงานวิชาคณิตศาสตร์ ซึ่งสร้างขึ้นมาเพื่อให้ผู้ที่สนใจได้ศึกษาหาความรู้เพิ่มเติม มิได้แสวงหาผลประโยชน์ใดๆทั้งสิ้น</b><br />
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<b>จัดทำโดย</b><br />
<b>นางสาวเกวลี ไตรวิทยาศิลป์ เลขที่ 38</b><br />
<b>นางสาวญาณภา สำราญถิ่น เลขที่ 39</b><br />
<b>ม.6/1</b></div>
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