Linear Algebra and Its Applications · Problem 1.3.7

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · gaussian-elimination

Problem

For which numbers

a

does elimination break down (a) permanently, and (b) temporarily?

\begin{aligned} ax + 3y &= -3 \\ 4x + 6y &= 6. \end{aligned}

Solve for

x

and

y

after fixing the second breakdown by a row exchange.