Suppose the vectors x_{1}, x_{2} and x_{3} ar | vedclass

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(D) Given that $Ax_{1} = b_{1}$,$Ax_{2} = b_{2}$,and $Ax_{3} = b_{3}$.We can combine these equations into a single matrix equation: $A[x_{1} \ x_{2} \

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$2$

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(D) Given that $Ax_{1} = b_{1}$,$Ax_{2} = b_{2}$,and $Ax_{3} = b_{3}$.We can combine these equations into a single matrix equation: $A[x_{1} \ x_{2} \ x_{3}] = [b_{1} \ b_{2} \ b_{3}]$.Let $X = [x_{1} \ x_{2} \ x_{3}] = \begin{bmatrix} 1 & 0 & 0 \ 1 & 2 & 0 \ 1 & 1 & 1 \end{bmatrix}$ and $B = [b_{1} \ b_{2} \ b_{3}] = \begin{bmatrix} 1 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 2 \end{bmatrix}$.Then $AX = B$,which implies $|A||X| = |B|$.Calculating the determinant of $X$: $|X| = 1(2 	imes 1 - 0 	imes 1) = 2$.Calculating the determinant of $B$: $|B| = 1(2 	imes 2 - 0 	imes 0) = 4$.Thus,$|A| 	imes 2 = 4$,which gives $|A| = 4/2 = 2$.

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