Can anyone help me with this elementary problem? How do I prove the following is a subspace?
W = {(a1, a2, a3) | 2*a1 - 7*a2 +a3 = 0}
I know I have to prove its closed under addition and multiplication... But the condition on W is confusing me...
Can anyone help me with this elementary problem? How do I prove the following is a subspace?
W = {(a1, a2, a3) | 2*a1 - 7*a2 +a3 = 0}
I know I have to prove its closed under addition and multiplication... But the condition on W is confusing me...
I think I just solved it, actually!
I let a3 = 7*a2 - 2*a1, and made that the new condition on W.
I then let a = (a1, a2, 7*a2 - 2*a1) and similarly for b.
Then I did a + cb = (a1 + c*b1, a2 + c*b2, 7(a2 + c*b2) - 2(a1 + c*b1))
Which satisfies my new condition on W I believe...
Can anyone verify this?