If A is invertible, then the columns of A 1 are linearly independent. Explain why. A. If A is invertible, then the rows of A are linearly independent, which implies that the columns of A¯' are linearly independent. B. The columns of A invertible and its columns are linearly independent. are linearly independent because A is a square matrix, and according to the Invertible Matrix Theorem, if a matrix is square, it is O C. According to the Invertible Matrix Theorem, if a matrix is invertible its columns form a linearly dependent set. When the columns of a matrix are linearly dependent, then the columns of the inverse of that matrix are linearly independent. Therefore, the columns of A are linearly independent. 1 O D. It is a known theorenm that if A is invertible then A must also be invertible. According to the Invertible Matrix Theorem, if a matrix is invertible its columns Click to select your answer.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
Problem 23EQ
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If A is invertible, then the columns of A
1
are linearly independent. Explain why.
A. If A is invertible, then the rows of A are linearly independent, which implies that the columns of A¯' are linearly independent.
B. The columns of A
invertible and its columns are linearly independent.
are linearly independent because A is a square matrix, and according to the Invertible Matrix Theorem, if a matrix is square, it is
O C. According to the Invertible Matrix Theorem, if a matrix is invertible its columns form a linearly dependent set. When the columns of a matrix are linearly
dependent, then the columns of the inverse of that matrix are linearly independent. Therefore, the columns of A are linearly independent.
1
O D. It is a known theorenm that if A is invertible then A
must also be invertible. According to the Invertible Matrix Theorem, if a matrix is invertible its columns
Click to select your answer.
Transcribed Image Text:If A is invertible, then the columns of A 1 are linearly independent. Explain why. A. If A is invertible, then the rows of A are linearly independent, which implies that the columns of A¯' are linearly independent. B. The columns of A invertible and its columns are linearly independent. are linearly independent because A is a square matrix, and according to the Invertible Matrix Theorem, if a matrix is square, it is O C. According to the Invertible Matrix Theorem, if a matrix is invertible its columns form a linearly dependent set. When the columns of a matrix are linearly dependent, then the columns of the inverse of that matrix are linearly independent. Therefore, the columns of A are linearly independent. 1 O D. It is a known theorenm that if A is invertible then A must also be invertible. According to the Invertible Matrix Theorem, if a matrix is invertible its columns Click to select your answer.
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