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Chapter 7: Q7-1E (page 382)

If 0 is an eigenvalue of a matrix A, then det A = 0.

Short Answer

Expert verified

True, det A = 0

Step by step solution

01

Define eigenvalue:

Eigenvalues are a set of specialized scales associated with a system of linear equations. The corresponding eigenvalue, often denoted by 位.

02

Explanation for the det A = 0:

If detA鈮�0i.e. the matrix is invertible, then the linear transformation whose matrix in a basis is A is an isomorphism, thus a monomorphism, Therefore, kerA={0} So, 0 is not an eigenvalue of A. Hence, if 0 is an eigenvalue of A then,detA=0

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