Problem 1066

Find the values of the variables for which the statement is true, if possible.

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

Solution:-

Two matrices are equal if they are the same size and is corresponding elements, position by position, are equal.

These matrices are the same size, 2×2.

Since these two matrices are equal, corresponding elements must be equal. So for w we get the following equation.

w + 6 = 1

Therefore, w = – 5. In a similar way we get x = -8.

In the same manner the other variables can be found.

y = 8

z = 4.