Solution:

$Let A=\left[\begin{array}{ccc}{1} & {1} & {1} \\ {3} & {-1} & {3} \\ {5} & {5} & {-4}\end{array}\right] \quad, \quad B=\left[\begin{array}{c}{6} \\ {10} \\ {3}\end{array}\right], \quad X=\left[\begin{array}{c}{x} \\ {y} \\ {z}\end{array}\right]$

$|A|=\left|\begin{array}{ccc}{1} & {1} & {1} \\ {3} & {-1} & {3} \\ {5} & {5} & {-4}\end{array}\right|$

$|A|=1(4-15)-1(-12-15)+1(15+5)$ …