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Suppose a is an n×n singular matrix. what is at least one eigenvalue of a equal to?

User LeSam
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Final answer:

A singular matrix must have at least one eigenvalue equal to zero, which is a fundamental property that connects the concept of singularity to eigenvalues in linear algebra.

Step-by-step explanation:

When dealing with an n × n singular matrix, it is important to understand the connection between singularity and eigenvalues. A matrix is singular if and only if its determinant is zero. By definition, an eigenvalue λ of a matrix A satisfies the equation det(A - λI) = 0, where I is the identity matrix of the same size as A. For a singular matrix, this implies that there must be at least one eigenvalue that is equal to zero since the determinant of A is zero. Therefore, if a matrix is singular, one of its eigenvalues is guaranteed to be zero. This is a fundamental property that connects the concepts of singularity and eigenvalues in linear algebra.

User Theran
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