Question

Find the standard matrix for the orthogonal projection of R^3 onto the span{a_1,a_2} and confirm that the matrix is idempotent? a_1=(3, -4, 1) a_2=(2,0,3)

Answer 1

\[\left[\begin{matrix}\frac{113}{257}&\frac{-84}{257} &\frac{96}{257} \\ \frac{-84}{257} & \frac{208}{257} &\frac{56}{257} \\\frac{96}{257} & \frac{56}{257} &\frac{193}{257} \end{matrix}\right]\]

Answer 2

Yeah that is the answer! how'd you get it though??

Answer 3

I found an orthogonal basis for the span

then I found the projection matrix for each basis vector of my span

then I added the two matrices

Answer 4

I can't get the answer for some reason.. did you use 1/a^t*a (a*a^T) for each vector?

Answer 5

then add them together sorry I meant a^T

Answer 6

did you find an orthogonal basis first

Answer 7

you should use \[\frac{v^Tv}{v\cdot v}\]

Answer 8

http://alturl.com/c5xiq

Answer 9

http://alturl.com/6ez98

Answer 10

Oh you used the gram schmidt process

Answer 11

okay thanks