Finding Matrix A of Orthogonal Projection onto Line L in R2

AI Thread Summary
To find the matrix A for the orthogonal projection onto the line L spanned by the vector [2 5]T in R2, the correct slope must be determined. The slope of the line represented by the vector is 5/2, not -2/5, indicating a misunderstanding in the initial calculations. Using the correct slope, the projection matrix formula is applied to derive the matrix A. The confusion arises from the incorrect line equation, which does not align with the vector's direction. Ultimately, accurately identifying the line's slope is crucial for constructing the correct projection matrix.
sonya
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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.
 
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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 ...
 
Your line is supposed to contain scalar multiples of [2 5]^T. Quick test-is [2 5]^T on the line 2x+5y = 0?
 
ok...now I'm really lost! I thought I made an equation from the given vector...so what do I do instead ?
 
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.
 

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