A First Course in Linear Algebra · Problem CRS.M10

Matrices — Robert Beezer

Mathematics — Linear Algebra · column-space-consistency

Problem

For the matrix

E

below, find vectors

\mathbf{b}

and

\mathbf{c}

so that the system

\mathcal{LS}(E, \mathbf{b})

is consistent and

\mathcal{LS}(E, \mathbf{c})

is inconsistent.

E = \begin{bmatrix} -2 & 1 & 1 & 0 \\ 3 & -1 & 0 & 2 \\ 4 & 1 & 1 & 6 \end{bmatrix}