SOLUTION: Let a be a fixed vector in R^3, and define W to be the subset of R^3 given by W={x: a^Tx=0}. Provce that W is a subspace of R^3.

Question 29494: Let a be a fixed vector in R^3, and define W to be the subset of R^3 given by
W={x: a^Tx=0}. Provce that W is a subspace of R^3.
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
Don't use a to represent a vector. I use u instead.
And u^T x means the inner (dot) product of
W={x: u^Tx=0}. Provce that W is a subspace of R^3.
proof: If x, y in W, a, b in R, then
u^T (ax+by) = a u^x + b u^y = 0
--> W is a subspace.
( = a + b &
= a + b called bilinear)
You have to work hard.
Kenny

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