Practice question · Multiple choice
A triangular matrix wears its eigenvalues on the diagonal, and a zero among them means the matrix is singular. Why do those two facts fit together?
Hints
- Write the determinant of a triangular matrix.
- Then write the determinant in terms of the eigenvalues.
Show the answer
A. Because the determinant is the product of the eigenvalues
Why
Both routes give the same number. A zero eigenvalue means some nonzero vector is sent to the origin, the map collapses a direction, which is singularity seen geometrically.
Practise Eigenvalues and Eigenvectors
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