Linear Algebra and Its Applications · Problem 1.3.27

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · gaussian-elimination

Problem

Find three values of

a

for which elimination breaks down, temporarily or permanently, in

\begin{aligned} au + u &= 1 \\ 4u + av &= 2. \end{aligned}

Breakdown at the first step can be fixed by exchanging rows—but not breakdown at the last step.