Hello,
Can you please help me figure this out?
Let <u,v> be the inner product on R2 generated by
[ 2 1 ]
[ 1 1 ]
<u+v,w>
u = (2,1)
v = (-1,1)
w = (0,-1)
....
I keep getting -2 is my answer, but the book states that it should be -7
$\displaystyle \displaystyle <u,w>=\left(\begin{bmatrix}
2 & 1\\
1 & 1
\end{bmatrix}\begin{bmatrix}
2\\
1
\end{bmatrix}\right)^T=\left(\begin{bmatrix}
2 & 1\end{bmatrix}\begin{bmatrix}
2 & 1\\
1 & 1
\end{bmatrix}\right)=\begin{bmatrix}
5 & 3\end{bmatrix}$
$\displaystyle \displaystyle \begin{bmatrix}
5 & 3\end{bmatrix}*Aw$
Do the same for the other one and add.