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

The equation is:

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

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When multiplying a matrix by 3, multiply each element by 3:

3$\begin{bmatrix} x & y \\ z & w \end{bmatrix}$ = $\begin{bmatrix} 3x & 3y \\ 3z & 3w \end{bmatrix}$

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When adding matrices, add the elements in the same position:

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

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

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

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The equation becomes:

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

When two matrices are equal, their corresponding elements must be equal. This gives four equations:

$3x = x + 4$

$3y = x + y + 6$

$3z = z + w - 1$

$3w = 2w + 3$

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From $3x = x + 4$:

$3x - x = 4$

$2x = 4$

$x = 2$

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From $3w = 2w + 3$:

$3w - 2w = 3$

$w = 3$

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From $3y = x + y + 6$, substituting $x = 2$:

$3y = 2 + y + 6$

$3y - y = 8$

$2y = 8$

$y = 4$

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From $3z = z + w - 1$, substituting $w = 3$:

$3z = z + 3 - 1$

$3z - z = 2$

$2z = 2$

$z = 1$

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Therefore, $x = 2$, $y = 4$, $z = 1$, and $w = 3$.