Finding Matrix A of Orthogonal Projection onto Line L in R2

[sonya]

Find the matrix A of the orthogonal projection onto the line L in R² that consists of all scalar multiples of the vector [2 5]^T .

OK...I really don't know how to start off with this problem. If somehow could just help me out there I will try to muddle my way through the rest ! Thanks.

 

[sonya]

OK...now I've thought about this...I should use the formula
1/(1+m²) [1 m ]
________[m m²]

using 2x+5y = 0 my slope m = -2/5

but my numbers come out backwards ...

 

[shmoe]

Your line is supposed to contain scalar multiples of [2 5]^T. Quick test-is [2 5]^T on the line 2x+5y = 0?

 

[sonya]

ok...now I'm really lost! I thought I made an equation from the given vector...so what do I do instead ?

 

[shmoe]

You do make a line from the vector. Find two points on the line spanned by the vector, (0,0) and (2,5) will work. The y-intercept is therefore 0 and the slope is (5-0)/(2-0)=5/2. The line you gave has -2/5, so something was off.