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## Homework Statement

Before I start, I should mention that I'm taking linear algebra in French so I hope I translated all the terms correctly. I'm studying for a test and here is a question I'm having a little trouble with...hope you can help!

U = span{[1 1 1 1]T, [-2 -2 1 1]T, [3 3 3 1]T, [0 0 1 0]T}

a) Calculate dim(U) and give a base of U.

b) Complete the base found in a) to obtain a base of R4.

## Homework Equations

## The Attempt at a Solution

a) I get a base of (-5/6, -1/3, -1/2, 1) so dim(U) has dim(U) = 1

b) This is where I don't know what to do. How to you complete a base? I don't need the answer, I just want to know how to complete a base. The only thought I had was to use the identity matrix but then again, I really don't know what to do or how to approach this. Any help is appreciated!