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If \( \begin{bmatrix} 2 & 3 \\[0.3em] 5& 7 \\[0.3em] \end{bmatrix}\)\( \begin{bmatrix} 1& -3 \\[0.3em] -2&4 \\[0.3em] \end{bmatrix}\) = \( \begin{bmatrix} -4& 6 \\[0.3em] -9&\text{x} \\[0.3em] \end{bmatrix}\) , find the value of x.

[(2,3)(5,7)] [(1,-3)(-2,4)] = [(-4,6)(-9,x)]

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Given : \( \begin{bmatrix} 2&3 \\[0.3em] 5& 7 \\[0.3em] \end{bmatrix}\)\( \begin{bmatrix} 1&-3 \\[0.3em] -2&4\\[0.3em] \end{bmatrix}\) = \( \begin{bmatrix} -4&6 \\[0.3em] -9&\text{x}\\[0.3em] \end{bmatrix}\) ,

To find : x

Formula used :

Where cij = ai1b1j + ai2b2j + ai3b3j + ……………… + ainbnj

Equating similar terms in the two matrices, we get

x = 13

x = 13

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