Mathematics 2019 JAMB Past Questions - Question 26: . Find the value of k if |-2 1 1| | 2 1 k|=23 | 1 2 -1|

Correct Answer

D

Explanation

To find the value of \( k \) in the matrix equation \( \begin{vmatrix} -2 & 1 & 1 \\ 2 & 1 & k \\ 1 & 2 & -1 \end{vmatrix} \), we can use the formula for the determinant of a 3x3 matrix:\[ \text{Determinant} = a(ei - fh) - b(di - fg) + c(dh - eg) \]Where the matrix is:\[ \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} \]In this case, the determinant is given as 23. We can expand the determinant using the given matrix and set it equal to 23 to solve for \( k \).After expanding the determinant and equating it to 23, we can solve for \( k \).