True or False question. (please provide short explanation) (e) If A is a diagonal 3 × 3 matrix with numbers d1 = 4 and d2 = −3 and d3 = 4 positioned along the main diagonal, then det A = −48. (f) If A is a 3 × 3 matrix, then det(5A) = 5 det A. (g) If A is a 3 × 3 matrix, then det(5A) = 125 det A. (h) If A is an n × n matrix containing a column consisting of zeroes only, then det A = 0.
True or False question. (please provide short explanation) (e) If A is a diagonal 3 × 3 matrix with numbers d1 = 4 and d2 = −3 and d3 = 4 positioned along the main diagonal, then det A = −48. (f) If A is a 3 × 3 matrix, then det(5A) = 5 det A. (g) If A is a 3 × 3 matrix, then det(5A) = 125 det A. (h) If A is an n × n matrix containing a column consisting of zeroes only, then det A = 0.
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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True or False question. (please provide short explanation)
(e) If A is a diagonal 3 × 3 matrix with numbers d1 = 4 and d2 = −3
and d3 = 4 positioned along the main diagonal, then det A = −48.
(f) If A is a 3 × 3 matrix, then det(5A) = 5 det A.
(g) If A is a 3 × 3 matrix, then det(5A) = 125 det A.
(h) If A is an n × n matrix containing a column consisting of zeroes
only, then det A = 0.
Expert Solution
Step 1 Introduction
Use basic properties of diagonal matrix and Determinants we get following results.
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