Evaluate the determinant: left|begin{array}{c | vedclass

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(D) Let $A = \left|\begin{array}{ccc} 3 & -4 & 5 \ 1 & 1 & -2 \ 2 & 3 & 1 \end{array}ight|$.Expanding along the first row $(R_1)$:$|A| = 3 \left|\

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$46$

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(D) Let $A = \left|\begin{array}{ccc} 3 & -4 & 5 \ 1 & 1 & -2 \ 2 & 3 & 1 \end{array}ight|$.Expanding along the first row $(R_1)$:$|A| = 3 \left|\begin{array}{cc} 1 & -2 \ 3 & 1 \end{array}ight| - (-4) \left|\begin{array}{cc} 1 & -2 \ 2 & 1 \end{array}ight| + 5 \left|\begin{array}{cc} 1 & 1 \ 2 & 3 \end{array}ight|$Calculating the $2 	imes 2$ determinants:$|A| = 3(1(1) - (-2)(3)) + 4(1(1) - (-2)(2)) + 5(1(3) - 1(2))$$|A| = 3(1 + 6) + 4(1 + 4) + 5(3 - 2)$$|A| = 3(7) + 4(5) + 5(1)$$|A| = 21 + 20 + 5 = 46$

Evaluate the determinant: $\left|\begin{array}{ccc} 3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1 \end{array}\right|$

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