Consider the following matrix A and its reduced row-echelon form: 3 -3 12 -6 -27 -24 1 -1 4 -2 -9 -8 3 6 -24 -15 18 21 -1 0 0 3 4 3 A = rref(A) = Basis for row(A). 1 0 0 -3 -4 -3 0 1-4 -1 5 5 000 0 0 0 0000 0 0 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 1 Jal

Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.4: Determinants
Problem 52PS
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Consider the following matrix A and its reduced row-echelon form:
-3 12 -6 -27 -24
-2 -9 -8
−1 4
3
6 -24 -15 18 21
-1 0 0 3 4 3
A =
3
0
H
0
Dimension of null(A): 1
Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them.
Dimension of row(A): 1
Basis for row(A):
Basis for null(A):
0
0
0
Dimension of col(A): 1
{}}
Basis for col(A):
rref(A) =
1 0 0 −3 −4 −3
01 -4 -1 5 5
000 0 00
000 0 0 0
Transcribed Image Text:Consider the following matrix A and its reduced row-echelon form: -3 12 -6 -27 -24 -2 -9 -8 −1 4 3 6 -24 -15 18 21 -1 0 0 3 4 3 A = 3 0 H 0 Dimension of null(A): 1 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 1 Basis for row(A): Basis for null(A): 0 0 0 Dimension of col(A): 1 {}} Basis for col(A): rref(A) = 1 0 0 −3 −4 −3 01 -4 -1 5 5 000 0 00 000 0 0 0
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