Asked by Selma Elzomor on May 09, 2024
Verified
Evaluate the determinant of the matrix. Expand by minors along the row or column that appears to make the computation easiest.
[−10−101012−2]\left[ \begin{array} { c c c } - 1 & 0 & - 1 \\0 & 1 & 0 \\1 & 2 & - 2\end{array} \right]−101012−10−2
A) 3
B) −1- 1−1
C) −3- 3−3
D) 222
E) 111
Determinant
A scalar value that can be computed from the elements of a square matrix and encodes certain properties of the matrix.
Minors
The determinants of the smaller square matrices obtained by removing one row and one column from a square matrix, used in calculating the determinant of the matrix.
- Evaluate determinants of 2x2 and 3x3 matrices.
Verified Answer
ML
McClain LasterMay 14, 2024
Final Answer :
A
Explanation :
Expanding along the second row, which contains two zeros, simplifies the calculation. The determinant is 0∗(−1)2+1∗∣0−12−2∣+1∗(−1)2+2∗∣−1−11−2∣=0+1∗((−1)∗(−2)−(−1)∗1)=1∗(2+1)=3.0*(-1)^{2+1}*\left|\begin{array}{cc}0 & -1 \\ 2 & -2\end{array}\right| + 1*(-1)^{2+2}*\left|\begin{array}{cc}-1 & -1 \\ 1 & -2\end{array}\right| = 0 + 1*((-1)*(-2) - (-1)*1) = 1*(2+1) = 3.0∗(−1)2+1∗02−1−2+1∗(−1)2+2∗−11−1−2=0+1∗((−1)∗(−2)−(−1)∗1)=1∗(2+1)=3.
Learning Objectives
- Evaluate determinants of 2x2 and 3x3 matrices.
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