Linear Algebra and Its Applications · Problem 1.2.9

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · geometry-of-linear-equations

Problem

The column picture for the previous exercise (singular system) is u[110]+v[121]+w[132]=b.u\begin{bmatrix}1\\1\\0\end{bmatrix} + v\begin{bmatrix}1\\2\\1\end{bmatrix} + w\begin{bmatrix}1\\3\\2\end{bmatrix} = b. Show that the three columns on the left lie in the same plane by expressing the third column as a combination of the first two. What are all the solutions (u,v,w)(u,v,w) if bb is the zero vector (0,0,0)(0,0,0)?

Browse the problem library