If 2begin{bmatrix} 5 & x 3 & 4 end{bmatrix} | vedclass

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Question

(A) Given the matrix equation: $2\begin{bmatrix} 5 & x \ 3 & 4 \end{bmatrix} + \begin{bmatrix} 0 & 1 \ 1 & y \end{bmatrix} = \begin{bmatrix} 10 & 5

Vedclass · Accepted Answer

$x = 2, y = -8$

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(A) Given the matrix equation: $2\begin{bmatrix} 5 & x \ 3 & 4 \end{bmatrix} + \begin{bmatrix} 0 & 1 \ 1 & y \end{bmatrix} = \begin{bmatrix} 10 & 5 \ 7 & 0 \end{bmatrix}$ First,multiply the first matrix by the scalar $2$: $\begin{bmatrix} 10 & 2x \ 6 & 8 \end{bmatrix} + \begin{bmatrix} 0 & 1 \ 1 & y \end{bmatrix} = \begin{bmatrix} 10 & 5 \ 7 & 0 \end{bmatrix}$ Now,add the two matrices on the left side: $\begin{bmatrix} 10+0 & 2x+1 \ 6+1 & 8+y \end{bmatrix} = \begin{bmatrix} 10 & 5 \ 7 & 0 \end{bmatrix}$ $\begin{bmatrix} 10 & 2x+1 \ 7 & 8+y \end{bmatrix} = \begin{bmatrix} 10 & 5 \ 7 & 0 \end{bmatrix}$ By comparing the corresponding elements: $2x + 1 = 5 \implies 2x = 4 \implies x = 2$ $8 + y = 0 \implies y = -8$ Therefore,$x = 2$ and $y = -8$.

If $2\begin{bmatrix} 5 & x \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 0 & 1 \\ 1 & y \end{bmatrix} = \begin{bmatrix} 10 & 5 \\ 7 & 0 \end{bmatrix}$,then find the values of $x$ and $y$.

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