Linear Algebra and Its Applications · Problem 1.3.8

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · gaussian-elimination

Problem

For which three numbers

k

does elimination break down? Which is fixed by a row exchange? In each case, is the number of solutions 0 or 1 or

\infty

\begin{aligned} kx + 3y &= 6 \\ 3x + ky &= -6. \end{aligned}