5. Diketahui \( D=\left[\begin{array}{ccc}8 & 5 & -1 \\ -2 & 3 & 3 \\ 12 & 6 & -4\end{array}\right] \), tentukanlah : \( \begin{array}{ll}\text { a. } \operatorname{det}(\mathrm{D}) & \text { b. } \operatorname{det}(2 \mathrm{D})\end{array} \)

Calculate the determinant of the matrix \( \begin{bmatrix} 8 & 5 & -1 \\ -2 & 3 & 3 \\ 12 & 6 & -4 \end{bmatrix} \). Matrices by following steps: - step0: Evaluate the determinant: \(\left[\begin{array}{rrr}{8}&{5}&{-1}\\{-2}&{3}&{3}\\{12}&{6}&{-4}\end{array}\right]\) - step1: Use the appropriate notation: \(\left|\begin{array}{cc}{8}&{5}&{-1}\\{-2}&{3}&{3}\\{12}&{6}&{-4}\end{array}\right|\) - step2: Use cofactor expansion along a row: \(8\times \left|\begin{array}{cc}{3}&{3}\\{6}&{-4}\end{array}\right|-5\times \left|\begin{array}{cc}{-2}&{3}\\{12}&{-4}\end{array}\right|-\left|\begin{array}{cc}{-2}&{3}\\{12}&{6}\end{array}\right|\) - step3: Evaluate the determinant: \(8\left(-30\right)-5\left(-28\right)-\left(-48\right)\) - step4: Evaluate: \(-240-\left(-140\right)+48\) - step5: Rewrite the expression: \(-240+140+48\) - step6: Add the numbers: \(-52\) a. \( \operatorname{det}(D) = -52 \) Next, let's calculate \( \operatorname{det}(2D) \). Matrices by following steps: - step0: Evaluate the determinant: \(\left[\begin{array}{rrr}{16}&{10}&{-2}\\{-4}&{6}&{6}\\{24}&{12}&{-8}\end{array}\right]\) - step1: Use the appropriate notation: \(\left|\begin{array}{cc}{16}&{10}&{-2}\\{-4}&{6}&{6}\\{24}&{12}&{-8}\end{array}\right|\) - step2: Use cofactor expansion along a row: \(16\times \left|\begin{array}{cc}{6}&{6}\\{12}&{-8}\end{array}\right|-10\times \left|\begin{array}{cc}{-4}&{6}\\{24}&{-8}\end{array}\right|-2\times \left|\begin{array}{cc}{-4}&{6}\\{24}&{12}\end{array}\right|\) - step3: Evaluate the determinant: \(16\left(-120\right)-10\left(-112\right)-2\left(-192\right)\) - step4: Evaluate: \(-1920-\left(-1120\right)+384\) - step5: Rewrite the expression: \(-1920+1120+384\) - step6: Add the numbers: \(-416\) b. \( \operatorname{det}(2D) = -416 \)