# Linear algebra: Basis, Nullspace, Subspace

• Dec 1st 2007, 09:18 PM
googoogaga
Linear algebra: Basis, Nullspace, Subspace
Your Help is greatly appreciated. Thanks in advance. I am having a hardtime with these three problems.

1) Find the basis for Nullspace of A if A equals

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

2) Let W be the subspace of R^(4) spanned by vectors (1,-2,5,3)^(T),
(2,3,1,-4)^(T), (3,8,-3,-5)^(T). Extend the basis of W to a basis of the whole space of R^(4).
• Dec 1st 2007, 09:50 PM
Jhevon
Quote:

Originally Posted by googoogaga
Your Help is greatly appreciated. Thanks in advance. I am having a hardtime with these three problems.

1) Find the basis for Nullspace of A if A equals

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

you have 2 problems here

The null space of a matrix $A$, is the set of all matrices $\bold{x}$ such that $A \bold{x} = \bold{0}$

thus you need to find the solution set to: $\left( \begin{array}{ccc} 1 & 2 & -3 \\ 2 & 1 & 0 \\ -2 & -1 & 3 \end{array} \right) \left( \begin{array}{c} x_1 \\ x_2 \\ x_3 \end{array} \right) = \left( \begin{array}{c} 0 \\ 0 \\ 0 \end{array} \right)$
• Dec 1st 2007, 10:33 PM
googoogaga
I now understand that Nullspace of A is (0, 0, 0)^(T), but what is the basis for the nullsapce. Was is a simple definition for basis, and how do you find it?