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

10 Find X Using Cramers Rulex 2y 3z 72x Y Z 43x 2y 2z 10 class=

Sagot :

Solution:

Given the system;

[tex]\begin{gathered} x-2y+3z=7 \\ \\ 2x+y+z=4 \\ \\ -3x+2y-2z=-10 \end{gathered}[/tex]

Thus;

[tex]\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}[/tex]

Also;

[tex]\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}[/tex]

Thus, the value of x is;

[tex]\begin{gathered} x=\frac{|X|}{|D|} \\ \\ x=\frac{30}{15} \\ \\ x=2 \end{gathered}[/tex]

ANSWER:

[tex]x=2[/tex]

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