Hey Guys on MHF.

I had a Basis and Subspace question and I was wondering if you could help check my answer and my working, and point me in the right direction if I've made a mistake.

The question is :

Exercise 1. Find a basis for the subspace W of R5 given by

W ={x∈R5 : x·a=x·b=x·c=0},

where a = (1,0,2,−1,−1), b = (2,1,1,1,0) and c = (4,3,−1,5,2). Determine the dimension

of W . (As usual, x · a denotes the dot (inner) product of the vectors x and a.)

The answer I ended up with was:

The basis of the subspace W = {(1,0,2,-1,1),(0,1,-3,3,2)}

& the dimension of W=2, as there are 2 vectors spanning in the subspace of W

My working out is here:

Part 1 : View image: part 1

Part 2 : http://s18.postimage.org/dfuxcdzi1/i...76476301_1.jpg

I was wondering if you guys could have a look at it for me!

It would greatly be appreciated