Given that the 4 x 5 matrix A below is row equivalent to the matrix U; A = 2 -4 4 2 6 1 -2 2 1 3 -1 2 1 -4 0 -2 4 -2 -4 0
Given that the 4 x 5 matrix A below is row equivalent to the matrix U; A = 2 -4 4 2 6 1 -2 2 1 3 -1 2 1 -4 0 -2 4 -2 -4 0
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 59EQ
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Question
Given that the 4 x 5 matrix A below is row equivalent to the matrix U;
A =
2 | -4 | 4 | 2 | 6 |
1 | -2 | 2 | 1 | 3 |
-1 | 2 | 1 | -4 | 0 |
-2 | 4 | -2 | -4 | 0 |
row equivalent ---->
U =
1 | -2 | 0 | 3 | 0 |
0 | 0 | 1 | -1 | 0 |
0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 0 | 0 |
1) What is the rank of A? What is the nullity of A?
2) Is the linear system Ax = b consistent for every b is an element of R4?
3) If the linear system Ax = b is consistent, how many solutions does it have, and how many parameters does it take to determine a solution?
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