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Extending a linearly set

  • Thread starter TiberiusK
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  • #1
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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?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi TiberiusK! :smile:

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

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