Linear Algebra and Its Applications · Problem 3.4.8

Orthogonality — Gilbert Strang

Mathematics · projection-non-orthogonal-vectors

Problem

Project the vector

b = (1, 2)

onto two vectors that are not orthogonal,

a_1 = (1, 0)

and

a_2 = (1, 1)

. Show that, unlike the orthogonal case, the sum of the two one-dimensional projections does not equal

b