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2. Let A and B be arbitrary 3 × 3 matrices. State "True" or "False" for each of the following statements. You do not need to justify your answers. (a) If|A| = -5, then A is invertible. (b) If |AB| = 0, then at least one of |A| and |B| must be zero. (c) If|A| = 0 and |B| = 0, then |A + B = 0. (d) If |A| = 0 and |B| = 0, then |AB| = 0. (e) |3A| = 3|A|. (f) |- A| = -|A|. (g) |A³|=|A|³. (h) If every entry of A is positive, then A is positive. (i) If every entry of A is an integer, then |A| is an integer. (j) A+B ≤|A| + |B|.

2. Let A and B be arbitrary 3 × 3 matrices. State "True" or "False" for each of the following statements. You do not need to justify your answers. (a) If|A| = -5, then A is invertible. (b) If |AB| = 0, then at least one of |A| and |B| must be zero. (c) If|A| = 0 and |B| = 0, then |A + B = 0. (d) If |A| = 0 and |B| = 0, then |AB| = 0. (e) |3A| = 3|A|. (f) |- A| = -|A|. (g) |A³|=|A|³. (h) If every entry of A is positive, then A is positive. (i) If every entry of A is an integer, then |A| is an integer. (j) A+B ≤|A| + |B|.

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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2. Let A and B be arbitrary 3 × 3 matrices. State "True" or "False" for each of the following statements. You do not need to justify your answers. (a) If|A| = -5, then A is invertible. (b) If |AB| = 0, then at least one of |A| and |B| must be zero. (c) If|A| = 0 and |B| = 0, then |A + B| = 0. (d) If |A| = 0 and |B| = 0, then |AB| = 0. (e) |3A| = 3|A|. (f) | A| = -|A|. (g) |A³|=|A|³. (h) If every entry of A is positive, then A is positive. (i) If every entry of A is an integer, then |A| is an integer. (j) A + B ≤|A| + |B|.
Transcribed Image Text:2. Let A and B be arbitrary 3 × 3 matrices. State "True" or "False" for each of the following statements. You do not need to justify your answers. (a) If|A| = -5, then A is invertible. (b) If |AB| = 0, then at least one of |A| and |B| must be zero. (c) If|A| = 0 and |B| = 0, then |A + B| = 0. (d) If |A| = 0 and |B| = 0, then |AB| = 0. (e) |3A| = 3|A|. (f) | A| = -|A|. (g) |A³|=|A|³. (h) If every entry of A is positive, then A is positive. (i) If every entry of A is an integer, then |A| is an integer. (j) A + B ≤|A| + |B|.
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