Determine whether the statement below is true or false. Justify the answer. If A is an invertible nxn matrix, then the equation Ax = b is consistent for each b in R". Choose the correct answer below. O A. The statement is false. The matrix A is invertible if and only if A is row equivalent to the identity matrix, and not every matrix A satisfying Ax = b is row equivalent to the identity matrix. B. The statement is false. The matrix A satisfies Ax = b if and only if A is row equivalent to the identity matrix, and not every matrix that is row equivalent to the identity matrix is invertible. O C. The statement is true. Since A is invertible, A'b = x for all x in R". Multiply both sides by A and the result is Ax = b. O D. The statement is true. Since A is invertible, A b exists for all b in R". Define x= Ab. Then Ax = b.

Determine whether the statement below is true or false. Justify the answer. If A is an invertible nxn matrix, then the equation Ax = b is consistent for each b in R". Choose the correct answer below. O A. The statement is false. The matrix A is invertible if and only if A is row equivalent to the identity matrix, and not every matrix A satisfying Ax = b is row equivalent to the identity matrix. B. The statement is false. The matrix A satisfies Ax = b if and only if A is row equivalent to the identity matrix, and not every matrix that is row equivalent to the identity matrix is invertible. O C. The statement is true. Since A is invertible, A'b = x for all x in R". Multiply both sides by A and the result is Ax = b. O D. The statement is true. Since A is invertible, A b exists for all b in R". Define x= Ab. Then Ax = b.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section: Chapter Questions

Problem 1RQ

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