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Explain solution for rd sharma class class 12 chapter Algebra of matrices exercise 4.3 question 24 sub question (ii) math

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Answer: x=13

Hint: Matrix multiplication is only possible, when the number of columns of first matrix is equal to the number of rows of second matrix.

Given: \left[\begin{array}{ll}2 & 3 \\ 5 & 7\end{array}\right]\left[\begin{array}{cc}1 & -3 \\ -2 & 4\end{array}\right]=\left[\begin{array}{cc}-4 & 6 \\ -9 & x\end{array}\right]

By multiplication of matrices, we have

\left[\begin{array}{ll}2(1)+3(-2) & 2(-3)+3(4) \\ 5(1)+7(-2) & 5(-3)+7(4)\end{array}\right]=\left[\begin{array}{ll}-4 & 6 \\ -9 & x\end{array}\right] \\\\ \left[\begin{array}{cc}2-6 & -6+12 \\ 5-14 & -15+28\end{array}\right] =\left[\begin{array}{cc}-4 & 6 \\ -9 & x\end{array}\right] \\\\\\ \left[\begin{array}{cc}-4 & 6 \\ -9 & 13\end{array}\right] =\left[\begin{array}{ll}-4 & 6 \\ -9 & x\end{array}\right]

Then, x=13

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