What is the value of a_{11}C_{11}+a_{12}C_{12}+a_{13}C_{13}?
Consider the following for the next three (03) items that follow : Let \Delta be the determinant of a matrix A, where A=\begin{pmatrix}a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\end{pmatrix} and C_{11}, C_{12}, C_{13} be the cofactors of a_{11}, a_{12}, a_{13} respectively.
- A. 0
- B. 1
- C. \Delta ✓
- D. -\Delta
Correct Answer: C. \Delta
Explanation
The sum of the products of the elements of any row (or column) of a determinant with their corresponding cofactors is equal to the value of the determinant, denoted by \Delta.
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