Let C be the following matrix: C=( 1 2 3 -2 0 1 1 -2 -1...

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.

Expert Solution

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

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.

milcah answered 1 year ago

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