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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?

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3BEXP
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Need help with this matrix algebra question. plese answer with Yes/No and explane why.

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? =
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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