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If $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ and $ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ , then X is equal to
If $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ and $ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ , then X is equal to
Updated On: Nov 19, 2024
- $ \left[ \begin{matrix} 5 & 0 \\ 0 & 4 \\ \end{matrix} \right] $
- $ \left[ \begin{matrix} 7 & 0 \\ 1 & 5 \\ \end{matrix} \right] $
- $ \left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right] $
- $ \left[ \begin{matrix} 7 & 1 \\ 0 & 4 \\ \end{matrix} \right] $
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The Correct Option is C
Solution and Explanation
Given, $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ ?.. (i) and
$ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ ..(ii)
On adding both equation, we get
$ 2X=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right]+\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 & 0 \\ 2 & 8 \\ \end{matrix} \right] $
$ \Rightarrow $ $ X=\left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right] $
$ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ ..(ii)
On adding both equation, we get
$ 2X=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right]+\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 & 0 \\ 2 & 8 \\ \end{matrix} \right] $
$ \Rightarrow $ $ X=\left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right] $
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Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
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