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}




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.


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