Linear Algebra and Its Applications · Problem 3.4.15

Orthogonality — Gilbert Strang

Mathematics · gram-schmidt-column-space

Problem

Find an orthonormal set

q_1

q_2

q_3

for which

q_1

q_2

span the column space of

A = \begin{bmatrix} 1 & 1 \\ 2 & -1 \\ -2 & 4 \end{bmatrix}.

Which fundamental subspace contains

q_3

? What is the least-squares solution of

Ax = b

b = [1\ 2\ 7]^T