9. Answer the following true/false questions and give explanations for each answer. (a) If a square matrix has an eigenvalue of 0 then the matrix is not invertible. (b) Suppose that A is a matrix with linearly independent columns and having the factorization A-QR then the matrix R is invertible. (c) If A is an eigenvalue of multiplicity 3, then is three-dimensional. (d) The eigenspace Ex of A is the same as the null space Nul(A-AI). (e) If A is diagonalizable, then A¹0 is also diagonalizable (f) If A and A' are row equivalent and det A'=0, then also det A=0. (g) If dim Nul(A)=0, then the columns of A are linearly independent. (h) If v₁, 2,.., 10 are vectors in R5, then the set of vectors is linearly dependent.

9. Answer the following true/false questions and give explanations for each answer. (a) If a square matrix has an eigenvalue of 0 then the matrix is not invertible. (b) Suppose that A is a matrix with linearly independent columns and having the factorization A-QR then the matrix R is invertible. (c) If A is an eigenvalue of multiplicity 3, then is three-dimensional. (d) The eigenspace Ex of A is the same as the null space Nul(A-AI). (e) If A is diagonalizable, then A¹0 is also diagonalizable (f) If A and A' are row equivalent and det A'=0, then also det A=0. (g) If dim Nul(A)=0, then the columns of A are linearly independent. (h) If v₁, 2,.., 10 are vectors in R5, then the set of vectors is linearly dependent.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 64CR: a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving...

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