Find a basis for a set S of R4

  • #1
ElijahRockers
Gold Member
270
10

Homework Statement



Find a basis for the subspace S of vectors (A+B, A-B+2C, B, C) in R4

What is the dimension of S?

The Attempt at a Solution



Do I just plug in varying values for A B and C to create four vectors, and see if they are linearly independent? If they are then I've found a basis?
 

Answers and Replies

  • #2
voko
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Making any two of A, B & C zero results in a vector in S. How many such vectors are there?
 
  • #3
LCKurtz
Science Advisor
Homework Helper
Insights Author
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Or, similar to voko's observation write it like this:$$
A(1,1,0,0)+B(1,-1,1,0)+C(0,2,0,1)$$and see if that helps.
 

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