Linear Algebra and Its Applications · Problem 1.3.4

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · gaussian-elimination

Problem

What multiple

\ell

of equation 1 should be subtracted from equation 2?

\begin{aligned} ax + by &= f \\ cx + dy &= g. \end{aligned}

The first pivot is

a

(assumed nonzero). Elimination produces what formula for the second pivot? What is

y

? The second pivot is missing when

ad = bc