Math Is Fun Forum

mathsforumhelp

Member

Registered: 2009-10-07

Posts: 14

Basis set

Consider the following sets of vectors in R3:

S1 =  { (3, -2, -3), (0, 4, 2), (0, 1, 3) } 
S2 =  { (-2, 3, 4), (2, 4, -3), (4, 3, -3), (4, 3, -2) } 
S3 =  { (0, -3, -4), (0, -12, 0), (0, 6, -12) } 
S4 =  { (-2, 2, 3), (4, -2, 3) } 

You are asked to determine which of these sets are bases for R3. For each of the following statements, select True or False to indicate your answer.   Help

1.  The set S1 is a basis for R3.   
2.  The set S2 is a basis for R3.   
3.  The set S3 is a basis for R3.   
4.  The set S4 is a basis for R3

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Basis set

Hi mathsforumhelp;

I am using a method that appears on wikipedia.

http://en.wikipedia.org/wiki/Basis_%28linear_algebra%29

1) True

Use the invertible matrix theorem:

Since the determinant of A is not 0 the columns of A form a basis for R3

2) False You need an n x n matrix to get a determinant.

3) False

Since the determinant of A is  0 the matrix is singular. The columns of A do not form a basis for R3

4) False

S4 is not a 3 x 3 matrix.

Last edited by bobbym (2009-10-07 21:41:34)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

mathsforumhelp

Member

Registered: 2009-10-07

Posts: 14

Re: Basis set

good answer thanks very much.