Exercise · ZW-COFACTOR-LAPLACE-EXPANSION-002 · ★☆☆ Basic
For the same matrix \(A=\begin{pmatrix}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 10\end{pmatrix}\), compute the minor \(M_{23}\) (no sign).
Choose one option.
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- D. \(-6\)
Explanation
Delete row 2 and column 3: \(\det\begin{pmatrix}1&2\\7&8\end{pmatrix}=8-14=-6\). The minor has no \((-1)^{i+j}\) factor; the cofactor \(C_{23}\) would be \(+6\).
Review the concept: Cofactor and Laplace expansion
The minor \(M\) of an entry is the determinant of the submatrix left after deleting its row and column; the cofactor \(C\) is that minor with an alternating sign.
\[C_{ij}=(-1)^{i+j}M_{ij}\]
More practice problems: cofactor and laplace expansion
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- ZW-COFACTOR-LAPLACE-EXPANSION-008 For A=[1 2 3; 4 5 6; 7 8 10], what is a_11C_21+a_12C_22+a_13C_23 (row 1 with the cofactors of row 2…
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