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Member

Registered: 2009-10-07

Posts: 14

Dimension of subspace

In R4 let

u1 = (0, 0, 0, -3), u2 = (0, 2, 3, -3), u3 = (-2, -4, -3, -3).
You are asked to determine the dimension of the subspace of R4 spanned by u1, u2, u3, and whether the set {u1, u2, u3} can be extended to a basis for R4.

1.  The set {u1, u2, u3} is linearly independent. 
2.  The dimension of the subspace span{u1, u2, u3} is     
3.  The number of vectors in any basis for R4 is   
4.  Select one of the radio buttons below and provide any additional information requested.
 

The set {u1, u2, u3} cannot be extended to a basis for R4.

The set {u1, u2, u3, w} is a basis for R4, where
w =

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Dimension of subspace

Hi;

3.  The number of vectors in any basis for R4 is

Answer to 3 is 4. The simplest is the standard basis

[1,0,0,0], [0,1,0,0], [0,0,1,0], [0,0,0,1] this is orthonormal and othogonal.

The set {u1, u2, u3, w} is a basis for R4, where
w =

One way to make  the set {u1, u2, u3, w} into a basis ( based on the invertible matrix theorem )

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

w = [1,1,1,1] but there are others.

Last edited by bobbym (2009-10-08 11:50:29)

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