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  • Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question  sub question (i)

Provide solution for rd sharma math class 12 chapter Algebra of matrices exercise 4.3 question sub question (i)

Answers (1)

Answer:  x=5 or -3 

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}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & -3\end{array}\right]\left[\begin{array}{l}x \\ 5\end{array}\right]=0

First, we multiply first two matrices

\begin {array}{ll}\Rightarrow\left[\begin{array}{ll}x-2 & 0-3\end{array}\right]\left[\begin{array}{l}x \\ 5\end{array}\right]=0 \\\ \Rightarrow\left[\begin{array}{ll}x-2 & -3\end{array}\right]\left[\begin{array}{l}x \\ 5\end{array}\right]=0\\\\ \Rightarrow[(x-2) x+5(-3)]=0 \\\\ \end{}

x^2 - 2x -15 = 0 then solve quadratic equation

\begin {array}{ll} \Rightarrow x^{2}-5 x+3 x-15=0 \\\\ \Rightarrow x(x-5)+3(x-5)=0\\ \\ \Rightarrow(x-5)(x+3)=0 \end {}

\begin {array}{ll} \Rightarrow Either \ \ x-5=0 \ \ or \ \ x+3=0 \\\\ \Rightarrow \quad x=5 \quad or \quad x=-3 \\\\So, x=5 \ \ or \ \ -3 \end {}

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