SOLUTION: The product of all the eigenvalues of the matrix A= [(1 2 1),(0 0 0),(1 0 1)] is

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Question 1176199: The product of all the eigenvalues of the matrix
A= [(1 2 1),(0 0 0),(1 0 1)] is
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The product of all eigenvalues of any square matrix is equal to its determinant.



For the given matrix, the product of all eigenvalues is equal to 0 (zero, ZERO),

since the determinant of the matrix is zero (BECAUSE it contains the zero row).


See this source
https://brilliant.org/discussions/thread/product-and-sum-of-eigenvalues/


Solved, answered and explained.