Question

question 5

---- is an eigenvalue of a if and only if a is singular.

Explanation:

Relate singularity to matrix invertibility

Using the Matrix Invertibility knowledge point

$$ \text{\(A\) is singular} \iff \det(A) = 0 $$

Relate determinant to eigenvalues

Using the Matrix Invertibility knowledge point

$$ \det(A) = \prod_{i=1}^{n} \lambda_i $$

Determine the required eigenvalue

Using the Matrix Invertibility knowledge point

$$ \det(A) = 0 \iff \lambda_i = 0 \text{ for some } i $$

Answer:

---- is an eigenvalue of A if and only if A is singular. <blank>0</blank>