Determine the product `[[-4, 4, 4], [-7, 1, 3],[5, -3, -1]][[1, -1, 1],[1, -2, -2],[2, 1, 3]]` and use it to solve the system of equations `x – y + z = 4, x – 2y – 2z = 9, 2x + y + 3z = 1`

Explanation

$${\left[\begin{array}{ccc}-4 & 4 & 4 \\ -7 & 1 & 3 \\ 5 & -3 & -1\end{array}\right]\left[\begin{array}{ccc}1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & 3\end{array}\right] }$$
$${\left[\begin{array}{ccc}(-4) \cdot 1+4.1+4.2 & (-4)(-1)+4(-2)+4.1 & (-4) \cdot 1+4(-2)+4.3 \\ (-7) \cdot 1+1.1+3.2 & (-7)(-1)+1 \cdot(-2)+3.1 & (-7) \cdot 1+1 \cdot(-2)+3.3 \\ 5.1+(-3) \cdot 1+(-1) \cdot 2 & 5(-1)+(-3)(-2)+(-1) \cdot 1 & 5.1+(-3)(-2)+(-1) \cdot 3\end{array}\right] }$$
$${\left[\begin{array}{lll}8 & 0 & 0 \\ 0 & 8 & 0 \\ 0 & 0 & 8\end{array}\right] }$$