Question

If AB=C,Matrices B and C of order
3 x 4 then order of Matrix A is *​

Answer 1

$\underline { \pink { Multiplication \:rule \:of \: matrices: }}</p><p>The<strong> </strong><strong>number</strong><strong> of</strong><strong> </strong><strong>colu</strong><strong>mns</strong><strong> </strong><strong>of</strong><strong> the</strong><strong> </strong><strong>1</strong><strong>s</strong><strong>t</strong><strong> </strong><strong>matrix</strong><strong> </strong><strong>must</strong><strong> </strong><strong>equa</strong><strong>l</strong><strong> </strong><strong>the</strong><strong> </strong><strong>number</strong><strong> of</strong><strong> </strong><strong>rows</strong><strong> </strong><strong>of</strong><strong> the</strong><strong> </strong><strong>2</strong><strong>n</strong><strong>d</strong><strong> </strong><strong>matrix</strong><strong> </strong><strong>.</strong><strong>And</strong><strong> </strong><strong>the</strong><strong> </strong><strong>result</strong><strong> </strong><strong>wi</strong><strong>ll</strong><strong> </strong><strong>have</strong><strong> </strong><strong>the</strong><strong> </strong><strong>s</strong><strong>ame</strong><strong> </strong><strong>n</strong><strong>umber</strong><strong> </strong><strong>of</strong><strong> </strong><strong>rows</strong><strong> </strong><strong>as</strong><strong> </strong><strong>the</strong><strong> </strong><strong>1</strong><strong>s</strong><strong>t</strong><strong> </strong><strong>matrix</strong><strong> </strong><strong>,</strong><strong>and</strong><strong> </strong><strong>the</strong><strong> </strong><strong>sa</strong><strong>me</strong><strong> </strong><strong>number</strong><strong> </strong><strong>of</strong><strong> </strong><strong>col</strong><strong>umns</strong><strong> </strong><strong>as</strong><strong> </strong><strong>the</strong><strong> </strong><strong>2</strong><strong>n</strong><strong>d</strong><strong> </strong><strong>matrix</strong><strong>.</strong></p><p>[tex] Let \: Order \:of \: matrix A = m \times n$

$Order \:of \: matrix B \: and \: C = 3 \times 4$

/* According to the rule */

$Number \:of \:rows \: of \: Matrix A \\= Number \:of \:rows \: of \: Matrix C$

$\implies m = 3$

$Number \:of \:columns \: of \: Matrix A \\= Number \:of \: rows \: of \: Matrix B$

$\implies n = 3$

Therefore.,

$\red { Order \: of \: Matrix \: A } \green { = 3 \times 3 }$

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