Assisted Computation: For each item, you are given a matrix A, its rref R, and the of A". (i) Find a basis for rowspace(A), colspace(A), and nullspace(A), if po using only the information found in A and R. (ii) Find a basis for nullspace(AT) only the information found in R'. Practice sight-reading the nullspaces. (iii) St rank and nullity of A and AT, and verify that the Dimension Theorem is satisfied b A and AT. (iv) Decide if A is full-rank or not. 3 2 8. 9. 5 6 2 1 а. А 7 6 4 b. A = -4 -7 5 2 16 29 6 -7 3 2 6 3

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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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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2.3 #1

Answer A and B

Assisted Computation: For each item, you are given a matrix A, its rref R, and the
of A". (i) Find a basis for rowspace(A), colspace(A), and nullspace(A), if pc
using only the information found in A and R. (ii) Find a basis for nullspace(AT)
only the information found in R'. Practice sight-reading the nullspaces. (iii) St=
rank and nullity of A and AT, and verify that the Dimension Theorem is satisfied b
A and AT. (iv) Decide if A is full-rank or not.
1.
3
2
8.
5
6 2 1
а. А :
5
7 6 4
b. A =
-4 -7 5 2
16 29 6 -7
2 6 3
1 0 4
5
1 0
4 0
R =
0 1 -2 -3
R
0 1 -3 0
%3D
0 0 0 0
0 0
1
1 0 -3
1 0 0
0 1 5
0 1 0
R' =
R' =
0 0 0
0 0 1
0 0 0
0 0 0
3.
Transcribed Image Text:Assisted Computation: For each item, you are given a matrix A, its rref R, and the of A". (i) Find a basis for rowspace(A), colspace(A), and nullspace(A), if pc using only the information found in A and R. (ii) Find a basis for nullspace(AT) only the information found in R'. Practice sight-reading the nullspaces. (iii) St= rank and nullity of A and AT, and verify that the Dimension Theorem is satisfied b A and AT. (iv) Decide if A is full-rank or not. 1. 3 2 8. 5 6 2 1 а. А : 5 7 6 4 b. A = -4 -7 5 2 16 29 6 -7 2 6 3 1 0 4 5 1 0 4 0 R = 0 1 -2 -3 R 0 1 -3 0 %3D 0 0 0 0 0 0 1 1 0 -3 1 0 0 0 1 5 0 1 0 R' = R' = 0 0 0 0 0 1 0 0 0 0 0 0 3.
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