Answer each of the following questions withjustification.(a) If A is a 5 x 6 matrix, can the columns of Aform a basis for R5.(b) If A, B, and C are n × n matrices, A isinvertible, and AB = AC, then must B = C?(c) If x is an eigenvector of the 4 x 4 matrix Acorresponding to the eigenvalue 2 = 0, do thecolumns of A span Rª?(d) If A is a 3 x 4 matrix, what is the largest valueof the rank of A? What is the largest value ofthe dimension of the null space of A?(e) Let A be a 4 x 4 matrix with det A = 6, and thematrix B is formed from A by firstinterchanging Rows two and three, and thendividing Row one by 2. What is det B?%3D

Answer each of the following questions with justification. (a) If A is a 5 x 6 matrix, can the columns of A form a basis for R5. (b) If A, B, and C are n x n matrices, A is invertible, and AB = AC, then must B = C? (c) If x is an eigenvector of the 4 x 4 matrix A corresponding to the eigenvalue 2 = 0, do the columns of A span R*? (d) If A is a 3 x 4 matrix, what is the largest value of the rank of A? What is the largest value of the dimension of the null space of A? (e) Let A be a 4 x 4 matrix with det A = 6, and the matrix B is formed from A by first interchanging Rows two and three, and then dividing Row one by 2. What is det B? %3D

Answer each of the following questions with justification. (a) If A is a 5 x 6 matrix, can the columns of A form a basis for R5. (b) If A, B, and C are n x n matrices, A is invertible, and AB = AC, then must B = C? (c) If x is an eigenvector of the 4 x 4 matrix A corresponding to the eigenvalue 2 = 0, do the columns of A span R*? (d) If A is a 3 x 4 matrix, what is the largest value of the rank of A? What is the largest value of the dimension of the null space of A? (e) Let A be a 4 x 4 matrix with det A = 6, and the matrix B is formed from A by first interchanging Rows two and three, and then dividing Row one by 2. What is det B? %3D

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section: Chapter Questions

Problem 1RQ

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