Given the following cases: (a) A is a 3 x 3 matrix with 3 pivot positions. (b) A is a 3 x 3 matrix with 2 pivot positions. (c) A is a 3 x 2 matrix with 2 pivot positions. (d) A is a 2 x 4 matrix with 2 pivot positions. For each of the cases above answer the following two questions. i. Does the equation Ax = 0 have a nontrivial solution? ii. Is the equation Ax = b consistent for every possible b?
Given the following cases: (a) A is a 3 x 3 matrix with 3 pivot positions. (b) A is a 3 x 3 matrix with 2 pivot positions. (c) A is a 3 x 2 matrix with 2 pivot positions. (d) A is a 2 x 4 matrix with 2 pivot positions. For each of the cases above answer the following two questions. i. Does the equation Ax = 0 have a nontrivial solution? ii. Is the equation Ax = b consistent for every possible b?
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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Transcribed Image Text:Given the following cases:
(a) A is a 3 x 3 matrix with 3 pivot positions.
(b) A is a 3 x 3 matrix with 2 pivot positions.
(c) A is a 3 x 2 matrix with 2 pivot positions.
(d) A is a 2 x 4 matrix with 2 pivot positions.
For each of the cases above answer the following two questions.
i. Does the equation Ax 0 have a nontrivial solution?
ii. Is the equation Ax = b consistent for every possible b?
=
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