Consider the following matrix A and its reduced row-echelon form: -2 6-2 2 -10 -10 -6 18 -4 4-24 -22 A = -2 6-1 1-7 -6 1 -3 0 0 2 1 0 0 1 0 1 5 0 0 1 -2 1 0 -1 3 -2 3 -10 -8 000000 - Find the dimensions of row(A), null(A), and im(A), and give a basis for each of them Dimension of row(A): 1 Basis for row(A): Dimension of null(A): 1 {:} 0 Basis for null(A): {B} 0 Dimension of im(A): 1 0 {8} Basis for im(A): rref(A) =

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Matrices And Determinants
Section: Chapter Questions
Problem 3T
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Consider the following matrix A and its reduced row-echelon form:
-2 6 -2 2 -10 -10
-6 18 -4 4 -24 -22
A =
-2 6 -1 1-7 -6
-1 3-2 3 -10 -8
Basis for row(A):
Find the dimensions of row(A), null(A), and im(A), and give a basis for each of them.
Dimension of row(A): 1
Dimension of null(A): 1
0
{8}]}
0
0
Basis for null(A):
{]}
Dimension of im(A): 1
0
{}}
Basis for im(A):
rref(A) =
1
-3 0 0 2 1
0 0 1 0 1 5
0001 -2 1
000000
Transcribed Image Text:Consider the following matrix A and its reduced row-echelon form: -2 6 -2 2 -10 -10 -6 18 -4 4 -24 -22 A = -2 6 -1 1-7 -6 -1 3-2 3 -10 -8 Basis for row(A): Find the dimensions of row(A), null(A), and im(A), and give a basis for each of them. Dimension of row(A): 1 Dimension of null(A): 1 0 {8}]} 0 0 Basis for null(A): {]} Dimension of im(A): 1 0 {}} Basis for im(A): rref(A) = 1 -3 0 0 2 1 0 0 1 0 1 5 0001 -2 1 000000
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