Given S= [a,b,c,d] belongs to R4, a not = 0. Find a basis that is a subset of s.
I am unsure what the a not = 0 means.
Would it just be a(1,0,0,0)+b(0,1,0,0)+c(0,0,1,0)+d(0,0,0,1) a not = 0.
If not, can someone give me an example of the basis.
Thanks in advance
Someone corrected my interpretation of this question. I though it was asking for a basis for the "subspace" S but in fact it is asking for a basis for consisting of vectors in the set S.
Try this: the standard basis for is <1, 0, 0, 0>, <0, 1, 0, 0>, <0, 0, 1, 0>, and <0, 0, 0, 1> where the last three are not from set S. Okay, just change the first component: try <1, 0, 0, 0>, <1, 1, 0, 0>, <1, 0, 1, 0>, and <1, 0, 0, 1>. Is that a basis for ? There are four vectors in it; are they independent?