Find a basis for the set of all vectors of the form (a-2b+5c,2a+5b-8c,-a-4b+7c,3a+b+c).
This made so much sense in the book.
lawrence wrote:So the basis is just ? It's that easy?
lawrence wrote:So this is where I have to do the vector-sum equals zero thing? When I solve the matrix, I get...
So a=-c, b=2c. If c=-1, then a=1,b=-2 and (1,2,-1,3)+(4,-10,8,-2)+(-5,8,-7,-1) = (0,0,0,0). So the answer is just the first two vectors, (1,2,-1,3),(-2,5,-4,1)?