Question

please answer this question fast. it's really urgent. ​

Answer 1

${\huge{\star{\underbrace{\tt{\red{Answer}}}}}}{\huge{\star}}$

(i) Let the order of matrix X be a × b .

$\sf \left[ \begin{array}{cc}2 & 1 \\ - 3 & 4 \end{array} \right] _{2 \times 2} \: \times \: x _{a \times b} = \left[ \begin{array}{c}7 & 6\end{array} \right] _{2 \times 1}$

${\sf{\implies{}}}$ a = 2 and b = 1

${\sf{\therefore{}}}$ The order of matrix X = a×b = 2×1

(ii)

$\sf \: Let \: matrix \: X =\left[ \begin{array}{c}x & y\end{array} \right]$

$\therefore \: \sf \left[ \begin{array}{cc}2 & 1 \\ - 3 & 4 \end{array} \right] \sf \left[ \begin{array}{c}x & y \end{array} \right] = \sf \left[ \begin{array}{c}7 & 6\end{array} \right]$

$\implies \: \sf \left[ \begin{array}{cc}2x + y \\ - 3x + 4y\end{array} \right] = \sf \left[ \begin{array}{c}7 & 6 \end{array} \right]$

$:\longmapsto \: \sf \: 2x + y = 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (i)$

$: \longmapsto \sf \: \: 3x + 4y = 6 \: \: \: \: \: \: \: \: \: \: \: \: (ii)$

On solving equations (i) and (ii) we get :

x = 2 and y = 2

$\therefore \sf The \: matrix \: X = \left[ \begin{array}{c}x & y \end{array} \right] = \left[ \begin{array}{c}2 & 3 \end{array} \right]$

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