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# Given 3[x y z w] = [ x 6 - 1 2w] + [4 x + y z + w 3], find the values of x, y, z and w.

Q12.    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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$3\begin{bmatrix}x & y \\ z & w \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix} + \begin{bmatrix} 4 &x + y \\ z + w & 3 \end{bmatrix}$

$\begin{bmatrix}3x &3 y \\3 z & 3w \end{bmatrix} = \begin{bmatrix} x+4 & 6+x+y \\ -1+z+w & 2w+3 \end{bmatrix}$

If two matrices are equal than corresponding elements are also equal.

Thus, we have

$3x=x+4$

$3x-x=4$

$2x=4$

$x=2$

$3y=6+x+y$

Put the value of x

$3y-y=6+2$

$2y=8$

$y=4$

$3w=2w+3$

$3w-2w=3$

$w=3$

$3z=-1+z+w$

$3z-z=-1+3$

$2z=2$

$z=1$

Hence, we have $x=2,y=4,z=1\, \, and\, \, w=3.$

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