Linear Algebra and Its Applications · Problem 3.3.13

Orthogonality — Gilbert Strang

Mathematics · least-squares-straight-line

Problem

Find the best straight-line fit (least squares) to the measurements

b = 4 \text{ at } t = -2, \quad b = 3 \text{ at } t = -1,

b = 1 \text{ at } t = 0, \quad b = 0 \text{ at } t = 2.

Then find the projection of

b = (4, 3, 1, 0)

onto the column space of

A = \begin{bmatrix} 1 & -2 \\ 1 & -1 \\ 1 & 0 \\ 1 & 2 \end{bmatrix}.