Given,
\( \begin{bmatrix}5 & -7 \\[0.3em]-2 & 3\\[0.3em]\end{bmatrix}\)\( \begin{bmatrix}x & y \\[0.3em]z & u\\[0.3em]\end{bmatrix}\)=\( \begin{bmatrix}-16 & -6 \\[0.3em]7 & 2\\[0.3em]\end{bmatrix}\)

Multiplying we get,

\( \begin{bmatrix}5x-7z & 5y-7u \\[0.3em]-2x+3z & -2y+3u\\[0.3em]\end{bmatrix}\)= \( \begin{bmatrix}-16 & -6 \\[0.3em]7 & 2\\[0.3em]\end{bmatrix}\)

From above we can see that,

5x – 7z = – 16 …(1) 

–2x + 3z = 7 ….(2) 

5y – 7u = – 6 …..(3)

–2y + 3u = 2 ……(4)

Now,

We have to solve these equations to find values of x, y, z and u Multiplying eq (1) by 2 and eq (2) by 5 and adding the equations we get,

10x – 14z + 10x + 15z = – 32 + 35

Z = 3

Putting this value in eq (1) we get,

5x – 21 = – 16 

5x = 5 

x = 1

Now, 

Multiplying eq (3) by 2 and eq (4) by 5 and adding we get,

10y – 14u + 10y + 15u = – 12 + 10

u = – 2

Putting value of u in equation (3) we get,

5 y + 14 = – 6 

5 y = – 20 

y = – 4

Therefore now we have,

\( \begin{bmatrix}x & y \\[0.3em]z & u\\[0.3em]\end{bmatrix}\)= \( \begin{bmatrix}1 &-4 \\[0.3em]3 &-2\\[0.3em]\end{bmatrix}\)