How do you find a basis for the null space of the matrix:

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- Mar 16th 2009, 05:28 PMantmanbasis for null space of matrix
How do you find a basis for the null space of the matrix:

- Mar 16th 2009, 09:13 PMThePerfectHacker
- Mar 17th 2009, 09:10 AMantman
Reduced matrix

- Mar 17th 2009, 12:08 PMThePerfectHacker
Given a matrix the nullspace is the set of all so that where is zero vector in . To find the nullspace you basically need to solve the homogenous equation . If you convert this problem in Gaussian-Jordan elimination, it means you need to solve the equation where was an attached coloumn of zeros (corresponding to the fact that we are solving a homogenous system). Therefore, you end up with (notice the new coloum of zeros):

This matrix is telling us that (the last two coloums do not tell us anything):

Thus,

.

If we let then:

Are always in the nullspace.

Thus, the nullspace is,

Can you find a basis now? - Mar 17th 2009, 07:47 PMantman
Would the basis just be { }