Question

10) find x using Cramer's rule:x - 2y + 3z = 72x + y + z = 4-3x + 2y - 2z = - 10

Answer 1

Given the system;

`\begin{gathered} x-2y+3z=7 \\ \\ 2x+y+z=4 \\ \\ -3x+2y-2z=-10 \end{gathered}`

Thus;

`\begin{gathered} D=\begin{bmatrix}{1} & {-2} & {3} \\ {2} & {1} & {1} \\ {-3} & {2} & {-2}\end{bmatrix} \\ \\ |D|=1(-2-2)+2(-4+3)+3(4+3) \\ \\ |D|=-4-2+21 \\ \\ |D|=15 \end{gathered}`

Also;

`\begin{gathered} X=\begin{bmatrix}{7} & {-2} & {3} \\ {4} & {1} & {1} \\ {-10} & {2} & {-2}\end{bmatrix} \\ \\ |X|=7(-2-2)+2(-8+10)+3(8+10) \\ \\ |X|=-28+4+54 \\ \\ |X|=30 \end{gathered}`

Thus, the value of x is;

`\begin{gathered} x=(|X|)/(|D|) \\ \\ x=(30)/(15) \\ \\ x=2 \end{gathered}`

ANSWER:

`x=2`