Chapter 3.10, Problem 2P

For the given sets of vectors, find the dimension of the space spanned by them and a basis for this space.

(a) $\left(1,-1,0,0\right),\left(0,-2,5,1\right),\left(1,-3,5,1\right),\left(2,-4,5,1\right);$

(b) $\left(0,1,2,0,0,4\right),\left(1,1,3,5,-3,5\right),\left(1,0,0,5,0,1\right),\left(-1,1,3,-5,-3,3\right),\left(0,0,1,0,-3,0\right);$

(c) $\left(0,10,-1,1,10\right),\left(2,-2,-4,0,-3\right),\left(4,2,0,4,5\right),\left(3,2,0,3,4\right),\left(5,-4,5,6,2\right).$