Thread: Spanning Set of Null Space

1. Spanning Set of Null Space

My teacher was out and so I didn't learn this, and yet I have a quiz on the material . . . please help!

Determine a spanning set for the null space of the given matrix:
1 2 3 5
1 3 4 2
2 4 6 -1

I would prefer directions or an explanation to an answer - I need to know how to do problems of this type, not this specific problem. Thanks!

2. Originally Posted by dan213
My teacher was out and so I didn't learn this, and yet I have a quiz on the material . . . please help!

Determine a spanning set for the null space of the given matrix:
1 2 3 5
1 3 4 2
2 4 6 -1

I would prefer directions or an explanation to an answer - I need to know how to do problems of this type, not this specific problem. Thanks!

Call your matrix $\displaystyle A$ ,then:

1) Solve the homogeneous linear system $\displaystyle Ax=0$ . This is the same as finding the null space of $\displaystyle A$:

2) As we know, the above solution is a linear subspace (in this case, of $\displaystyle \mathbb{F}^4\,,\,\mathbb{F}=$ some field) , so now you can choose some spanning set, or even some basis, for it.

Tonio