Linear Algebra and Its Applications · Problem 1.3.31

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · gaussian-elimination

Problem

For which three numbers

a

will elimination fail to give three pivots?

\begin{aligned} ax + 2y + 3z &= b_1 \\ ax + ay + 4z &= b_2 \\ ax + ay + az &= b_3. \end{aligned}