Question

Ob Ос Question 10 2 pts a. If L is a line through O and if is the orthogonal projection of y onto L, then |||| gives the distance from y to L. False. The distance from y to Lis given by y- b. True. The value | || of gives the distance from y to L and is the orthogonal projection. True. The value of ||0|| gives the distance from y to Lwhich is equivalent to y-D.. False. The distance from y to Lis given by lly-pl c. d. a Question 11 3 pts

Answer 1

Given that, 'L' is a line through 0.

$\hat{y }$ is the orthogonal projection of 'y' onto 'L' .

Let, 'L' is generated by a single vector 'v'.

Then,

$\hat{y}= Proj_L (y)= \frac{<v,y>}{<v,v>} v$

which is another vector along 'L'. Then, || $\hat{y }$ || gives the magnitude of that vector. The statement is FALSE.

The distance from 'y' to 'L' =  $||y- \hat{y}||$

Option d is correct.