1. Determine if the statement is true or false. If it is true, explain why. If it is false, provide a counterexample or an explanation. (a) Let T : R" → R" be a linear transformation. If T is one-to-one then n < m. (b) For all square matrices A and B. it is true that det(A+ B) = det A + det B.
1. Determine if the statement is true or false. If it is true, explain why. If it is false, provide a counterexample or an explanation. (a) Let T : R" → R" be a linear transformation. If T is one-to-one then n < m. (b) For all square matrices A and B. it is true that det(A+ B) = det A + det B.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 10EQ: In Exercises 7-10, give a counterexample to show that the given transformation is not a linear...
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