(b) Let A be a 5 x 5 matrix. Assume that the nullspace of A has dimension 2, show that 0 is an eigenvalue of AT with algebraic multiplicity at least 2. (c) Let A be a 5 x 7 matrix. (i) What is the maximum and minimum possible values of rank (A)? (ii) What is the maximum and minimum possible values of rank (AT)? Justify your answers.
(b) Let A be a 5 x 5 matrix. Assume that the nullspace of A has dimension 2, show that 0 is an eigenvalue of AT with algebraic multiplicity at least 2. (c) Let A be a 5 x 7 matrix. (i) What is the maximum and minimum possible values of rank (A)? (ii) What is the maximum and minimum possible values of rank (AT)? Justify your answers.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.2: Diagonalization
Problem 32E
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