Let A be a matrix, and let R be the RREF of the matrix. Determine a basis for each indicated space. If you do not need a vector, then place the number 0 in all boxes for that vector (for example, if you only need 3 vectors, then place 0 for all boxes that correspond to the last 2 vectors). 4 -4 -4 -2 -2 -2 0 -2 -2 0 -2 -2 1 4 -10 -10 -1 -7 -7 1 -2 0 A = -4 -4 16 16 0 12 12, R 00 0 0 1 -2 -2 -4 6 6 -2 6 6 000 0 0 0 2 2 1 -2 -2 0000000 1) The basis for Col(A) would be: 2) The basis for Row(A) would be: 3) The basis for Nul(A) would be: 100 C 7700
Let A be a matrix, and let R be the RREF of the matrix. Determine a basis for each indicated space. If you do not need a vector, then place the number 0 in all boxes for that vector (for example, if you only need 3 vectors, then place 0 for all boxes that correspond to the last 2 vectors). 4 -4 -4 -2 -2 -2 0 -2 -2 0 -2 -2 1 4 -10 -10 -1 -7 -7 1 -2 0 A = -4 -4 16 16 0 12 12, R 00 0 0 1 -2 -2 -4 6 6 -2 6 6 000 0 0 0 2 2 1 -2 -2 0000000 1) The basis for Col(A) would be: 2) The basis for Row(A) would be: 3) The basis for Nul(A) would be: 100 C 7700
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:Let A be a matrix, and let R be the RREF of the matrix. Determine a basis for each indicated space. If you do not need a vector, then place the number 0
in all boxes for that vector (for example, if you only need 3 vectors, then place 0 for all boxes that correspond to the last 2 vectors).
4
-2
-2 -2 -2
1
0 -2 -2 0 -2
-4 -4
-10 -10 -1 -7
4
1
-7
0
1
-2 -2 0 -1
A = -4
-4
16
16
0
12
12 |, R = 0 0
0
0
0 1
-2
1
-4 6
6
-2
6
6
0
0
0
0 0
0
-2 2
2
1
-2
-2
0
0
0
0
0
0
1) The basis for Col(A) would be:
2) The basis for Row(A) would be:
3) The basis for Nul(A) would be:
ๆ
* -
* *
0
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