5. State whether the following are True or FalseWith a valid explanation,(a) For any 3 × 3 matrix A and nonzero real number A, we have rank(AA) = rank(A).(b) If A and B are any 2 × 2 matrices such that ABmatrices C.0, then ACB= 0 for all 2 × 2(c) It is possible for a linear transformation f : R? → R² that is not the identity to beboth a rotation and a scaling transformation.

We are given three statements to check if it is true or false with valid explanations.

5. State whether the following are True or False With a valid explanation, (a) For any 3 × 3 matrix A and nonzero real number A, we have rank(AA) = rank(A). (b) If A and B are any 2 x 2 matrices such that AB = 0, then ACB : matrices C. (c) It is possible for a linear transformation ƒ : R² → R² that is not the identity to be both a rotation and a scaling transformation. O for all 2 x 2

5. State whether the following are True or False With a valid explanation, (a) For any 3 × 3 matrix A and nonzero real number A, we have rank(AA) = rank(A). (b) If A and B are any 2 x 2 matrices such that AB = 0, then ACB : matrices C. (c) It is possible for a linear transformation ƒ : R² → R² that is not the identity to be both a rotation and a scaling transformation. O for all 2 x 2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 55EQ

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