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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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 × 2 matrices such that AB matrices 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 be both a rotation and a scaling transformation.
Transcribed Image Text: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 × 2 matrices such that AB matrices 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 be both a rotation and a scaling transformation.
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