0 votes 0 votes Consider the $3 \times 3$ matrix $\boldsymbol{M}=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6\end{array}\right]$. The determinant of $\left(\boldsymbol{M}^{2}+12 \boldsymbol{M}\right)$ is $\_\_\_\_\_\_\_\_\_$. Linear Algebra gate-ds-ai-2024 numerical-answers matrix determinant linear-algebra + – Arjun asked Feb 16 • recategorized 4 days ago by Arjun Arjun 670 views answer comment Share Follow See 1 comment See all 1 1 comment reply ankitgupta.1729 commented Feb 16 reply Follow Share Since row transformation $R_3 \leftarrow R_3-(R_1+R_2)$ makes $\det(M)=0$ Hence, $\det(M^2+12M)=\det(M(M+12I))=\det(M)\det(M+12I)=0$ $\because \det(AB)=\det(A)\det(B)$ where A and B are square matrices of the same order. 1 votes 1 votes Please log in or register to add a comment.
0 votes 0 votes determinant is 0 liontig37 answered Feb 17 liontig37 comment Share Follow See all 0 reply Please log in or register to add a comment.