Ok, Linear Algebra question here. I have no idea what I'm exactly doing wrong, or how everyone else does this. I can't find a good example online that is doing it the way my text book is teaching it.
So here's the problem.
Let L be the line in R^3 that consists of all scalar multiples of
L=*this is a 1x3 matrix, not sure how to represent a matrix well on here*Code:2 1 2
Find the reflection of the vector about the line L.
v=*again, 1x3 matrix*Code:1 1 1
From what I know, I need to find the orthogonal projection of v onto line L, and then use a handy dandy formula.
I know that a projection is equal to ;
(1/||w||^2)w dot w^T
where ||w||^2 is the magnitude of w squared and w^T is w transpose.
So, I'm saying that w is my line, L. Therefore, ||w||^2 = ((2^2 + 1^2 + 2)^1/2)^2 = ((9)^1/2)^2) = 9
and L dot L^T = 3x3 matrix;SoOoOOoOo my projection matrix, A, is equal toCode:4 2 4 2 1 2 4 2 4
(1/9) *And my handy dandy formula to find the reflection of a matrix with respect to a line is 2proj(x) - x which is alsoCode:4 2 4 2 1 2 4 2 4
2Ax - x
(2A - I)x where I is an identity matrix
preforming this out is definitely not getting me the answer in the back of the book though.
I apologize for this really weird way of typing this out, and I really dunno what I'm seeing incorrectly but it's something massive lol.