Math, asked by arifaislam784, 1 month ago

Please someone help with this class 10 sum​

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Answered by BrainlyFlash
1

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(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 = 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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Hope it's help

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