Given that the matrix A is row equivalent to U: 2 3 4 -2 5 4 05 -1 0 0 0 0 -4 5 -3 A = U 011 4 -4 1 -1 then you should be able to answer the following without doing any row operations. (a) Find a basis for the row space of A. (b) Find a basis for the column space of A. (c) What are the rank and the nullity of A? (d) What are the rank and the nullity of AT?
Given that the matrix A is row equivalent to U: 2 3 4 -2 5 4 05 -1 0 0 0 0 -4 5 -3 A = U 011 4 -4 1 -1 then you should be able to answer the following without doing any row operations. (a) Find a basis for the row space of A. (b) Find a basis for the column space of A. (c) What are the rank and the nullity of A? (d) What are the rank and the nullity of AT?
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 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...
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![1. Given that the matrix A is row equivalent to U:
2
3
4
-2 5
4
-4
5 -3
05 -1
A =
U =
0 11
0 0
0 0
5
4
-4
1
-1
then you should be able to answer the following without doing any row operations.
(a) Find a basis for the row space of A.
(b) Find a basis for the column space of A.
(c) What are the rank and the nullity of A?
(d) What are the rank and the nullity of AT?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8d14a18-18b6-4b9f-91b0-8c8acc9b34e2%2F0955e987-1532-4b63-b3f5-637cfa29ce54%2Fwl3wzv6_processed.png&w=3840&q=75)
Transcribed Image Text:1. Given that the matrix A is row equivalent to U:
2
3
4
-2 5
4
-4
5 -3
05 -1
A =
U =
0 11
0 0
0 0
5
4
-4
1
-1
then you should be able to answer the following without doing any row operations.
(a) Find a basis for the row space of A.
(b) Find a basis for the column space of A.
(c) What are the rank and the nullity of A?
(d) What are the rank and the nullity of AT?
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