Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. If the columns of A are linearly dependent, then det A = 0. Choose the correct answer below. O A. The statement is false. The columns of I are linearly dependent, yet det I = 1. O B. The statement is false. If det A = 0, then A is invertible. OC. The statement is true. If the columns of A are linearly dependent, then one of the columns is equal to another. O D. The statement is true. If the columns of A are linearly dependent, then A is not invertible.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
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Chapter6: Linear Systems
Section6.5: Determinants
Problem 90E
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Let A be an n×n matrix. Determine whether the statement below is true or false. Justify the answer.
If the columns of A are linearly​ dependent, then det
A=0.
Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
If the columns of A are linearly dependent, then det A = 0.
Choose the correct answer below.
O A. The statement is false. The columns of I are linearly dependent, yet det I = 1.
B. The statement is false. If det A = 0, then A is invertible.
OC. The statement is true. If the columns of A are linearly dependent, then one of the columns is equal to another.
D. The statement is true. If the columns of A are linearly dependent, then A is not invertible.
Transcribed Image Text:Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. If the columns of A are linearly dependent, then det A = 0. Choose the correct answer below. O A. The statement is false. The columns of I are linearly dependent, yet det I = 1. B. The statement is false. If det A = 0, then A is invertible. OC. The statement is true. If the columns of A are linearly dependent, then one of the columns is equal to another. D. The statement is true. If the columns of A are linearly dependent, then A is not invertible.
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