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.
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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 25E
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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.
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