Dimension of subspace given Vectors

• Mar 12th 2009, 06:27 AM
needshelp12
Dimension of subspace given Vectors
Hello Everyone,

I have been given 4 vectors [1 2 3 0], [2 3 0 4], [5 0 6 7], [8 5 9 11] and been asked to find the dimension of the subspace spanned by the vectors listed above.

I have gone ahead and put these vectors into a matrix

1 2 3 0
2 3 0 4
5 0 6 7
8 5 9 11

I have proceeded to reduce these to row echelon form but am unsure of what I should do next?

any insight or help would be greatly appreciated.

Thanks
• Mar 12th 2009, 07:02 AM
HallsofIvy
Quote:

Originally Posted by needshelp12
Hello Everyone,

I have been given 4 vectors [1 2 3 0], [2 3 0 4], [5 0 6 7], [8 5 9 11] and been asked to find the dimension of the subspace spanned by the vectors listed above.

I have gone ahead and put these vectors into a matrix

1 2 3 0
2 3 0 4
5 0 6 7
8 5 9 11

I have proceeded to reduce these to row echelon form but am unsure of what I should do next?

any insight or help would be greatly appreciated.

Thanks

Presumably you row reduced as way of determining how many of the vectors were independent. The dimension of the span of these vectors is the number of independent vectors- the number of non-zero rows in the reduced matrix.
• Mar 12th 2009, 07:19 AM
needshelp12
alright so given that i have row reduced the matrix to get the matrix below

1 2 3 0
0 -1 -6 4
5 -1 0 11
0 0 0 0

I know now that x1 x2 and x3 are all linearly dependent, now how do i know what the dimension of the subspace spanned is?
• Mar 12th 2009, 07:24 AM
needshelp12
sorry not X1 X2 X3 i meant v1 v2 v3 and v4 are linearly dependent