I am not sure regarding this question. i am supposed to decide if 2 claims are true,false or only one is correct.
i've solved it, but not sure it's correct. would appreciate your opinions.
1)let $W=sp({2x+1,x^2})$ be a subspace of $R_3[x]x$ with the inegral inner product in [0,1], so {40x^2-44x+9} is a basis for $W^\bot$.
2)let $w=sp{(1,i,1),(1+i,0,2)}$ be a subspace of $C^3$, so {(1+i,1,-1)} is a basis for $W^\bot$.
both are correct if i calculated right. both sp's are linearly indepenent and they do seem to create a basis for $W^\bot$ (scalar product of 0). what i got is okie?
Both are correct. It's straight forward calculation that verifies the given vectors belong to the given perpendicular components. Since each $W$ is of dimension $2$ (since they're spanned by $2$ linearly independent vectors), it follows that each $W^\perp$ is dimension $1$, so a single non-zero vector will span them.