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IntroAnalysis
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Homework Statement
For the system Ax = b, find least squares solution.
A = (1 2) ; b = (3, 2, 1)T
----(2 4)
----(1 -2)
Homework Equations
I know if A is an m x n matrix of rank n, the normal equations
ATAx = ATb
have a unique solution x = (ATA)-1ATb
However, the matrix A is not linearly independent, and is only rank = 1.
Using Gaussian elimination, I think this system of equations is inconsistent. But book gives
answer {(1 - 2α, α)T; α real}
I don't see how they get this. Aren't these the equations of 3 parallel lines?