Given 3begin{bmatrix} x & y z & w end{bmatri | vedclass

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(A) Given the matrix equation: $3\begin{bmatrix} x & y \ z & w \end{bmatrix} = \begin{bmatrix} x & 6 \ -1 & 2w \end{bmatrix} + \begin{bmatrix} 4 & x

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$x=2, y=4, z=1, w=3$

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(A) Given the matrix equation: $3\begin{bmatrix} x & y \ z & w \end{bmatrix} = \begin{bmatrix} x & 6 \ -1 & 2w \end{bmatrix} + \begin{bmatrix} 4 & x+y \ z+w & 3 \end{bmatrix}$ Multiplying the scalar $3$ into the first matrix: $\begin{bmatrix} 3x & 3y \ 3z & 3w \end{bmatrix} = \begin{bmatrix} x+4 & 6+x+y \ -1+z+w & 2w+3 \end{bmatrix}$ By equating the corresponding elements of the matrices: $1) \ 3x = x + 4 \Rightarrow 2x = 4 \Rightarrow x = 2$ $2) \ 3y = 6 + x + y \Rightarrow 2y = 6 + 2 = 8 \Rightarrow y = 4$ $3) \ 3w = 2w + 3 \Rightarrow w = 3$ $4) \ 3z = -1 + z + w \Rightarrow 2z = -1 + 3 = 2 \Rightarrow z = 1$ Thus,the values are $x=2, y=4, z=1, w=3$.

Given $3\begin{bmatrix} x & y \\ z & w \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix} + \begin{bmatrix} 4 & x+y \\ z+w & 3 \end{bmatrix}$,find the values of $x, y, z$ and $w$.

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