Extending Linearly Independent Vectors to Create a Basis in R^4

[TiberiusK]

Homework Statement

Let u1 = (2; 1; 1; 1) and u2 = (4; 2; 2;-1).I need to extend the linearly independent set u1 and u2 to obtain a basis of R^4.

Homework Equations

The Attempt at a Solution

u1 and u2 are linearly independent since both vectors are non-zero and none is a multiple of the other ,I should probably choose 2 other vector u3 and u4 such that I have a matrix of rank 4,since R^4, and to keep the linearly independece ...but what should I do next?Can someone please explain to me?

 

[tiny-tim]

Hi TiberiusK!

(try using the X² and X₂ icons just above the Reply box )

u1 and u2 are linearly independent since both vectors are non-zero and none is a multiple of the other ,I should probably choose 2 other vector u3 and u4 such that I have a matrix of rank 4,since R^4, and to keep the linearly independece ...but what should I do next?Can someone please explain to me?

any two vectors will do …

choose the simplest you can think of (and of course check that all four are linearly independent)