Question

Basis of Null Space Question with trivial solution: see attachment

Answer 1

Question

Answer 2

i thought the answer will be a set of zero vectors but it says i am wrong please help?

Answer 3

@zepdrix

Answer 4

The basis of the nullspace is the set of vectors such that when you multiply the matrix with any linear combinations of those vectors, you get the zero vector.

Answer 5

In other words, it asks for the basis for the set of vectors \(\mathbf{x}\) such that \(M\mathbf{x}=0\).

Answer 6

If you are wondering, yes it is in some sense the exact opposite of finding the basis for the image of the matrix.

Answer 7

im a little lost

Answer 8

Not surprised given how poorly I phrased it lol. For a given matrix M, there will be a set of vectors such that Mx=0. Correct?

Answer 9

yes

Answer 10

The basis of the nullspace is the basis for that aforementioned set.