Question

In: Advanced Math

Find a basis of U = span {(1,1,2,3), (2,4,1,0), (1,5,-4,-9)}

Expert Solution

Row
Operation
1:

1	2	1
1	4	5
2	1	-4
3	0	-9

add -1 times the 1st row to the 2nd row

1	2	1
0	2	4
2	1	-4
3	0	-9

Row
Operation
2:

1	2	1
0	2	4
2	1	-4
3	0	-9

add -2 times the 1st row to the 3rd row

1	2	1
0	2	4
0	-3	-6
3	0	-9

Row
Operation
3:

1	2	1
0	2	4
0	-3	-6
3	0	-9

add -3 times the 1st row to the 4th row

1	2	1
0	2	4
0	-3	-6
0	-6	-12

Row
Operation
4:

1	2	1
0	2	4
0	-3	-6
0	-6	-12

multiply the 2nd row by 1/2

1	2	1
0	1	2
0	-3	-6
0	-6	-12

Row
Operation
5:

1	2	1
0	1	2
0	-3	-6
0	-6	-12

add 3 times the 2nd row to the 3rd row

1	2	1
0	1	2
0	0	0
0	-6	-12

Row
Operation
6:

1	2	1
0	1	2
0	0	0
0	-6	-12

add 6 times the 2nd row to the 4th row

1	2	1
0	1	2
0	0	0
0	0	0

Row
Operation
7:

1	2	1
0	1	2
0	0	0
0	0	0

add -2 times the 2nd row to the 1st row

1	0	-3
0	1	2
0	0	0
0	0	0

Colby Messinger answered 1 year ago

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