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3. Consider the matrir [1 2 1 1 A = 3 7 3 3 2 2 3 4 (a) Are the columns of A linearly dependent or linearly independent? Justify your answer. The columns are linearly dependent: any set of four vectors in R are linearly dependent, so we don't even need to do any calculations to check this. (b) For what values of n and m does the matrir A determine a linear transformation T:R" + R". (c) Is the linear transformation T with standard matriz A one-to-one or onto? Justify your answer.

3. Consider the matrir [1 2 1 1 A = 3 7 3 3 2 2 3 4 (a) Are the columns of A linearly dependent or linearly independent? Justify your answer. The columns are linearly dependent: any set of four vectors in R are linearly dependent, so we don't even need to do any calculations to check this. (b) For what values of n and m does the matrir A determine a linear transformation T:R" + R". (c) Is the linear transformation T with standard matriz A one-to-one or onto? Justify your answer.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 31EQ
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3. Consider the matrir [1 2 1 1 A = 3 7 3 3 2 2 3 4 (a) Are the columns of A linearly dependent or linearly independent? Justify your answer. The columns are linearly dependent: any set of four vectors in R* are linearly dependent, so we don't even need to do any calculations to check this. (b) For what values of n and m does the matrir A determine a linear transformation T:R" + R". (c) Is the linear transformation T with standard matriz A one-to-one or onto? Justify your answer.
Transcribed Image Text:3. Consider the matrir [1 2 1 1 A = 3 7 3 3 2 2 3 4 (a) Are the columns of A linearly dependent or linearly independent? Justify your answer. The columns are linearly dependent: any set of four vectors in R* are linearly dependent, so we don't even need to do any calculations to check this. (b) For what values of n and m does the matrir A determine a linear transformation T:R" + R". (c) Is the linear transformation T with standard matriz A one-to-one or onto? Justify your answer.
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