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, V2,.., 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, V2,.., 10 are vectors in R5, then the set of vectors is linearly dependent.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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part h. it should be v_1, then, v_2, all the way to v_10 that spans r5
Transcribed Image Text: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.
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