AI Tutor
Back to Orthogonal least squares

Exercise 1

Avg difficulty 2.5

Suppose we write the linear system [1−12−1−13]x=[−85−10]\begin{bmatrix} 1 & -1 \\ 2 & -1 \\ -1 & 3 \end{bmatrix} \xvec = \threevec{-8}5{-10} as Ax=bA\xvec=\bvec.

  1. Find an orthogonal basis for Col(A)\col(A).

  2. Find b^\bhat, the orthogonal projection of b\bvec onto Col(A)\col(A).

  3. Find a solution to the linear system Ax=b^A\xvec = \bhat.

Austin, Understanding Linear Algebra, §6.5 Orthogonal least squares, Exercise 1

AI Tutor

Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.