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For each of the following, determine if the statement is true or false. justify your answer. a) If (, 2, a} is linearly independent, then (, 2} is also linearly independent. b) The columns of any 4 x 5 matrix are linearly dependent. c) Let T be a linear transformation. If T() = T(), then = j.

For each of the following, determine if the statement is true or false. justify your answer. a) If (, 2, a} is linearly independent, then (, 2} is also linearly independent. b) The columns of any 4 x 5 matrix are linearly dependent. c) Let T be a linear transformation. If T() = T(), then = j.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 3EQ: In Exercises 1-12, determine whether T is a linear transformation. T:MnnMnn defines by T(A)=AB,...
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For each of the following, determine if the statement is true or false. justify your answer. a) If {, 2, va} is linearly independent, then (ü, ü2} is also linearly independent. b) The columns of any 4 x 5 matrix are linearly dependent. c) Let T be a linear transformation. If T() = T(), then = j.
Transcribed Image Text:For each of the following, determine if the statement is true or false. justify your answer. a) If {, 2, va} is linearly independent, then (ü, ü2} is also linearly independent. b) The columns of any 4 x 5 matrix are linearly dependent. c) Let T be a linear transformation. If T() = T(), then = j.
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