calculation problems regarding computing distance from sub spaces

mathsnoob1

New member
Joined
Aug 12, 2017
Messages
4
hello,

i am having computation problems regarding computing distance from sub spaces. could you check if you get the same results as me please?

1)in R^3 the distance of v=(1,-1,2) from subspace W=sp{(0,1,1), (0,1,0)} equals 1.

2)in M_{2s2} ^R the distance from \begin{pmatrix}1&-1\\ 1&4\end{pmatrix} to w=sp{(\begin{pmatrix}1&-1\\ 0&2\end{pmatrix},\begin{pmatrix}1&0\\ 0&2\end{pmatrix}} is \sqrt151.

3)the normal of A=\begin{pmatrix}1&2\\ 3&-4\end{pmatrix} is \sqrt30 (A \in M_{2x2}^R)

and a small question if i may: is (a1b1+...anbn)^2 \le (less equal) (|a1|^2+...+|an|^2)(|b1|^2+...+|bn|^2)? (seems to hold true based on the triangle inequality, since using || ascertains we'll be getting a positive value, and it's just an application of multiplying both sides of the inequality by ()^2).

thank you very much for your kind help!

(if you get a different answer than me, please tell me so and write what you get, so i'll know if i've done a mistake)
 
Top