in each part, use the given inner product on R^2 to find || w|| where w=(-1,3) a)the Euclidean inner product b) the weighted Euclidean inner product = 3u1v1+2u2v2 where u =(u1,v1) and v=(v1,v2) c) the inner product generated by the matrix (top: 1,2; bottom: -1,3) I don't understand the question. Please tell me what they want me to do?

Question

in each part, use the given inner product on R^2 to find || w|| where w=(-1,3)
a)the Euclidean inner product
b) the weighted Euclidean inner product <u,v> = 3u1v1+2u2v2 where u =(u1,v1) and v=(v1,v2)
c) the inner product generated by the matrix (top: 1,2; bottom: -1,3)
I don't understand the question. Please tell me what they want me to do?

anonymous · Answer

$$
||w||=<w,w>=3(w_1)(w_1)+2(w_2)(w_2)
$$

anonymous · Answer

thats part (b)

anonymous · Answer

got it

anonymous · Answer

par a

anonymous · Answer

= sqtr(10)

anonymous · Answer

I'm ok withc

anonymous · Answer

(c):
obtain w'
$$w'=\left[\begin{matrix}1&2\-1&3\end{matrix}\right]\left[\begin{matrix}-1\3\end{matrix}\right]$$

anonymous · Answer

a) is it right? I got c) (know how to get)

anonymous · Answer

let me rearrange mine: a) = sqr(10) . is it right? everybody?

anonymous · Answer

b) and c) is quite easy, I got it. just want to confirm a

anonymous · Answer

if you take square-root, it is the L2 norm!

anonymous · Answer

what if in part b, it's not +, but -? I mean what if the problem ask for finding d(u,v) , base on the inner product they give out <u, v> = 3u1v1+2u2v2