5 votes 5 votes The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is$-1$$0$$1$$2$ Linear Algebra gatecse2024-set1 linear-algebra eigen-value + – Arjun asked Feb 16 • retagged Apr 26 by Arjun Arjun 3.3k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes Product of eigen values is Determinant of the matrix.Since, Columns are Linearly Dependent (C3 = 2*C2 - C1) we can say Determinant will be zero.(B) is correct option. himanshud2611 answered Feb 16 himanshud2611 comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Product of eigen values is the determinant of the matrix. Here the rows are linearly dependent as follows: row3 = 2*row2 - row1 Thus, the determinant is zero. Answer: option B aniketwaghela answered Feb 16 aniketwaghela comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes All columns of the matrix are Linearly Dependant on each other, so the determinant is 0. Hence the correct answer is B. pritam48cse answered Feb 16 pritam48cse comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes B)0 Krishna._.Bethina answered Feb 16 Krishna._.Bethina comment Share Follow See all 0 reply Please log in or register to add a comment.