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# Finding the nullspace... am I doing the right thing? watch

1. The question asks to find the special solutions to Mx=0 and to describe in words N(M). Am I doing the right thing?

Edit: Further to that, would N(M) be a subspace of R4?
2. (Original post by Plagioclase)
The question asks to find the special solutions to Mx=0 and to describe in words N(M). Am I doing the right thing?

Edit: Further to that, would N(M) be a subspace of R4?
I am a little rusty so sorry if I'm wrong but you have found the rref of the matrix and used the fact that the nullspace of a matrix is the same as the nullspace of the rref of said matrix. Then you have found a basis for the nullspace of the matrix so any element in the nullspace can be represented as a linear combination of the two vectors s1, s2 you have this is the plane you mention.

So yeah you are doing the right thing.

As to whether it is a subspace then is there perhaps a theorem you can think of about kernels and subspaces? If not think of the subspace test

i) is the zero element in the nullspace?
ii) is the nullspace closed under addition and multiplcation?

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Updated: February 21, 2016
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