If \[2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\] , find x − y.

\[2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\] \[ \Rightarrow \begin{bmatrix}6 + 1 & 8 + y \\ 10 + 0 & 2x + 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\] \[ \Rightarrow \begin{bmatrix}7 & 8 + y \\ 10 & 2x + 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}\] \[ \Rightarrow 8 + y =\text{ 0 and }2x + 1 = 5\] \[ \Rightarrow y =\text{- 8 and } 2x = 4\] \[ \Rightarrow y =\text{ - 8 and } x = 2\] \[Hence, x - y = 2 - ( - 8) = 10 .\]

If 2 [ 3 4 5 X ] + [ 1 Y 0 1 ] = [ 7 0 10 5 ] , Find X − Y. - Mathematics

Question

If $2 [\begin{matrix} 3 & 4 \\ 5 & x \end{matrix}] + [\begin{matrix} 1 & y \\ 0 & 1 \end{matrix}] = [\begin{matrix} 7 & 0 \\ 10 & 5 \end{matrix}]$ , find x − y.

Sum

Solution

$2 [\begin{matrix} 3 & 4 \\ 5 & x \end{matrix}] + [\begin{matrix} 1 & y \\ 0 & 1 \end{matrix}] = [\begin{matrix} 7 & 0 \\ 10 & 5 \end{matrix}]$

$\Rightarrow [\begin{matrix} 6 + 1 & 8 + y \\ 10 + 0 & 2 x + 1 \end{matrix}] = [\begin{matrix} 7 & 0 \\ 10 & 5 \end{matrix}]$

$\Rightarrow [\begin{matrix} 7 & 8 + y \\ 10 & 2 x + 1 \end{matrix}] = [\begin{matrix} 7 & 0 \\ 10 & 5 \end{matrix}]$

$\Rightarrow 8 + y = 0 and 2 x + 1 = 5$

$\Rightarrow y = - 8 and 2 x = 4$

$\Rightarrow y = - 8 and x = 2$

$H e n c e, x - y = 2 - (- 8) = 10 .$

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Algebraic Operations on Matrices - Addition of Matrices

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Chapter 5: Algebra of Matrices - Exercise 5.6 [Page 64]

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Chapter 5 Algebra of Matrices
Exercise 5.6 | Q 57 | Page 64

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If 2 [ 3 4 5 X ] + [ 1 Y 0 1 ] = [ 7 0 10 5 ] , Find X − Y. - Mathematics

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