Find the value of \left ( x-y \right )  form the matrix equation.
2\begin{bmatrix} x & 5\\ 7 & y-3 \end{bmatrix}+\begin{bmatrix} -3 & -4\\ 1 & 2 \end{bmatrix}= \begin{bmatrix} 7 & 6\\ 15 & 14 \end{bmatrix}\cdot

 

 

 

 
 
 




 

 

Answers (1)

2\begin{bmatrix} x & 5\\ 7& y-3 \end{bmatrix}+\begin{bmatrix} -3 & -4\\ 1& 2 \end{bmatrix}= \begin{bmatrix} 7 & 6\\ 15& 14 \end{bmatrix}
\Rightarrow \begin{bmatrix} 2x & 10\\ 14& 2y-6 \end{bmatrix}= \begin{bmatrix} 7 & 6\\ 15& 14 \end{bmatrix}- \begin{bmatrix} -3 & -4\\ 1& 2 \end{bmatrix}
\Rightarrow \begin{bmatrix} 2x & 10\\ 14& 2y-6 \end{bmatrix}= \begin{bmatrix} 10 & 10\\ 14& 12 \end{bmatrix}
By equality of matrices . we get : 2x= 10,2y-6= 12
\Rightarrow x= 5,y= 9 \; \; \; \therefore x-y= 5-9= -4

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