nd a basis for the column space of A. What dimension is the column space? 3) Find a basis for the null space of A. What dimension is the null space? 4) What is the rank of A? What is the nullity of A? 5) Is the linear system Ax = b consistent for every b is an element of R4? 6) 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?
nd a basis for the column space of A. What dimension is the column space? 3) Find a basis for the null space of A. What dimension is the null space? 4) What is the rank of A? What is the nullity of A? 5) Is the linear system Ax = b consistent for every b is an element of R4? 6) 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?
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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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) Find a basis for the row space of A. What dimension is the row space?
2) Find a basis for the column space of A. What dimension is the column space?
3) Find a basis for the null space of A. What dimension is the null space?
4) What is the rank of A? What is the nullity of A?
5) Is the linear system Ax = b consistent for every b is an element of R4?
6) 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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