(a) The matrices A and B below are row-equivalent (you do not have to veri. bases for Row(B), for Col(B) and for Null(B), and state their dimensions. N is needed. 01 4 0 6 0 0 0001500 A=0.000040 B = 00000 00003 0000000 3 i. Basis for Row(B) and dimension? ii. Basis for Col(B) and dimension? iii. Basis for Null(B) and dimension? 0-2 0 0 0 0 LEXAN 8 -1 -17 8 5 49 -8 53 -24 85 16 32 1 40 16 54 24 32 (b) Answer TRUE, FALSE or NONSENSE: i. For any mátrix A with reduced row echelon form B, we have Col(A) = Co ii. For any matrix A with reduced row echelon form B, we have Row(A) = R iii. For any matrix A with reduced row echelon form B, we have Null(A) = Nr
(a) The matrices A and B below are row-equivalent (you do not have to veri. bases for Row(B), for Col(B) and for Null(B), and state their dimensions. N is needed. 01 4 0 6 0 0 0001500 A=0.000040 B = 00000 00003 0000000 3 i. Basis for Row(B) and dimension? ii. Basis for Col(B) and dimension? iii. Basis for Null(B) and dimension? 0-2 0 0 0 0 LEXAN 8 -1 -17 8 5 49 -8 53 -24 85 16 32 1 40 16 54 24 32 (b) Answer TRUE, FALSE or NONSENSE: i. For any mátrix A with reduced row echelon form B, we have Col(A) = Co ii. For any matrix A with reduced row echelon form B, we have Row(A) = R iii. For any matrix A with reduced row echelon form B, we have Null(A) = Nr
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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Transcribed Image Text:2. (Basis, dimension)
(a) The matrices A and B below are row-equivalent (you do not have to verify this). Give
bases for Row(B), for Col(B) and for Null(B), and state their dimensions. No justification
is needed.
=
01
000 150
600
0
0
0.00004
0000003
0000000
i. Basis for Row(B) and dimension?
ii. Basis for Col(B) and dimension?
iii. Basis for Null(B) and dimension?
0 2
0
4
5
0
8
1
0 10
5
0 4 16 4
8
16
32
(A) + det(B).
1
17 8
49
53
85
8
0
9
3
6
24
4-32 21
(b) Answer TRUE, FALSE or NONSENSE:
i. For any mátrix A with reduced row echelon form B, we have Col(A) = Col(B).
ii. For any matrix A with reduced row echelon form B, we have Row(A) = Row(B).
iii. For any matrix A with reduced row echelon form B, we have Null(A) = Null(B).
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