If A = begin{bmatrix} 1 & 1 & -2 2 & 1 & -3 | vedclass

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(C) Given the matrix $A = \begin{bmatrix} 1 & 1 & -2 \ 2 & 1 & -3 \ 5 & 4 & -9 \end{bmatrix}$.To find the determinant $|A|$,we expand along the firs

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$0$

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(C) Given the matrix $A = \begin{bmatrix} 1 & 1 & -2 \ 2 & 1 & -3 \ 5 & 4 & -9 \end{bmatrix}$.To find the determinant $|A|$,we expand along the first row:$|A| = 1 \begin{vmatrix} 1 & -3 \ 4 & -9 \end{vmatrix} - 1 \begin{vmatrix} 2 & -3 \ 5 & -9 \end{vmatrix} + (-2) \begin{vmatrix} 2 & 1 \ 5 & 4 \end{vmatrix}$Calculating the $2 	imes 2$ determinants:$|A| = 1((1)(-9) - (-3)(4)) - 1((2)(-9) - (-3)(5)) - 2((2)(4) - (1)(5))$$|A| = 1(-9 + 12) - 1(-18 + 15) - 2(8 - 5)$$|A| = 1(3) - 1(-3) - 2(3)$$|A| = 3 + 3 - 6$$|A| = 6 - 6 = 0$Thus,the value of $|A|$ is $0$.

If $A = \begin{bmatrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{bmatrix}$,find $|A|$.

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