Explain why the columns of an nxn matrix A are linearly independent when A is invertible. Choose the correct answer below. O A. If A is invertible, then the equation Ax = 0 has the unique solution x = 0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent O B. IfA is invertible, then for all x there is ab such that Ax = b. Since x = 0 is a solution of Ax = 0, the columns of A must linearly independent. O C. If A is invertible, then A has an inverse matrix A1. Since AA-1 =A-'A, A must have linearly independent columns. O D. If A is invertible, then A has an inverse matrix A-1. Since AA-1 =I, A must have linearly independent columns.

Explain why the columns of an nxn matrix A are linearly independent when A is invertible. Choose the correct answer below. O A. If A is invertible, then the equation Ax = 0 has the unique solution x = 0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent O B. IfA is invertible, then for all x there is ab such that Ax = b. Since x = 0 is a solution of Ax = 0, the columns of A must linearly independent. O C. If A is invertible, then A has an inverse matrix A1. Since AA-1 =A-'A, A must have linearly independent columns. O D. If A is invertible, then A has an inverse matrix A-1. Since AA-1 =I, A must have linearly independent columns.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Explain why the columns of annxn matrix A are linearly independent when A is invertible.
Choose the correct answer below.
O A. If A is invertible, then the equation Ax = 0 has the unique solution x = 0. Since Ax = 0 has only the trivial solution, the columns of A must be linearly independent.
O B. If A is invertible, then for all x there is ab such that Ax = b. Since x = 0 is a solution of Ax = 0, the columns of A must be linearly independent.
O C. If A is invertible, then A has an inverse matrix A1. Since AA
'=AA, A must have linearly independent columns.
O D. If A is invertible, then A has an inverse matrix A. Since AA=I, A must have linearly independent columns.

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