Using properties of determinants, prove that: Given that: and , find . Using this result, solve the…

Using properties of determinants, prove that: $\begin{vmatrix} a & b & b+c \\ c & a & c+a \\ b & c & a+b \end{vmatrix} = (a + b + c)(a - c)^2$

Given that: $A = \begin{pmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 2 & -1 & 5 \end{pmatrix}$, find $AB$. Using this result, solve the following system of equation: $x - y = 3$, $2x + 3y + 4z = 17$ and $y + 2z = 7$