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How do you find the dimension of the subspace of R4 consisting of the vectors a plus 2b plus c b-2c 2a plus 2b plus c 3a plus 5b plus c?
Evil131313
The dimension of a space is defined as the number of vectors in its basis.
Assuming your vectors are
1,2,1,0
0,1,-2,0
2,2,1,0
and
3,5,1,0
(extra zeros because you are in R4)
then you must first check to see if they are linearly indepent. If all the vectors are linearly independent then the subspace defined by those vectors has a dimension 4, as there are 4 vectors in the basis.
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∙ 14y ago
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