Linear Algebra and Its Applications · Problem 3.4.12

Orthogonality — Gilbert Strang

Mathematics · gram-schmidt-qr

Problem

What multiple of

a_1 = \begin{bmatrix} 1 \\ 1 \end{bmatrix}

should be subtracted from

a_2 = \begin{bmatrix} 4 \\ 0 \end{bmatrix}

to make the result orthogonal to

a_1

? Factor

\begin{bmatrix} 1 & 4 \\ 1 & 0 \end{bmatrix}

into

QR

with orthonormal vectors in

Q