Finding Matrix A of Orthogonal Projection onto Line L in R2

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Homework Help Overview

The discussion revolves around finding the matrix A for the orthogonal projection onto a line L in R2, defined by scalar multiples of the vector [2 5]T. Participants are exploring the relationship between the vector and the line's equation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using a formula for the projection matrix and question the correctness of their calculations. There is a focus on deriving the line's equation from the given vector and verifying its properties.

Discussion Status

Some participants are attempting to clarify the relationship between the vector and the line's equation, while others are questioning their assumptions about the slope and the line's definition. There is an ongoing exploration of how to correctly represent the line based on the vector provided.

Contextual Notes

Participants are grappling with the implications of the line's equation and the vector's role in defining it. There is confusion regarding the slope derived from the vector and its consistency with the line's equation.

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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