In: Math
Let C be the following matrix:
C=( 1 2 3 -2
0 1 1 -2
-1 3 2 -8
-1 -2 -3 2 )
Give a basis for the row space of Cin the format [1,2,3],[3,4,5],
for example.
The matrix C is as under:
1 |
2 |
3 |
-2 |
0 |
1 |
1 |
-2 |
-1 |
3 |
2 |
-8 |
-1 |
-2 |
-3 |
2 |
To determine a basis for the row space of C, we will reduce it to its RREF as under:
Add 1 times the 1st row to the 3rd row
Add 1 times the 1st row to the 4th row
Add -5 times the 2nd row to the 3rd row
Add -5 times the 2nd row to the 3rd row
Then the RREF of C is
1 |
0 |
1 |
2 |
0 |
1 |
1 |
-2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
This implies that the first 2 rows of C are linearly independent. Also, the set{(1,2,3,-2), (0,1,1,-2)} or the set { (1,0,1,2),(0,1,1,-2)} is a basis for the row space of C.