If x begin{bmatrix} 2 3 end{bmatrix} + y beg | vedclass

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Question

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

Vedclass · Accepted Answer

$x=3, y=-4$

Vedclass · Answer

(A) Given the matrix equation: $x \begin{bmatrix} 2 \ 3 \end{bmatrix} + y \begin{bmatrix} -1 \ 1 \end{bmatrix} = \begin{bmatrix} 10 \ 5 \end{bmatrix}$ Multiplying the scalars $x$ and $y$ into the matrices,we get: $\begin{bmatrix} 2x \ 3x \end{bmatrix} + \begin{bmatrix} -y \ y \end{bmatrix} = \begin{bmatrix} 10 \ 5 \end{bmatrix}$ Adding the matrices on the left side: $\begin{bmatrix} 2x - y \ 3x + y \end{bmatrix} = \begin{bmatrix} 10 \ 5 \end{bmatrix}$ By comparing the corresponding elements,we obtain a system of linear equations: $1) \ 2x - y = 10$ $2) \ 3x + y = 5$ Adding equation $(1)$ and $(2)$: $(2x - y) + (3x + y) = 10 + 5$ $5x = 15$ $x = 3$ Substituting $x = 3$ into equation $(2)$: $3(3) + y = 5$ $9 + y = 5$ $y = 5 - 9$ $y = -4$ Thus,the values are $x = 3$ and $y = -4$.

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

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