Linear Algebra and Its Applications · Problem 1.3.25

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · gaussian-elimination

Problem

Apply elimination to the system u+v+w=−23u+3v−w=6u−v+w=−1.\begin{aligned} u + v + w &= -2 \\ 3u + 3v - w &= 6 \\ u - v + w &= -1. \end{aligned} When a zero arises in the pivot position, exchange that equation for the one below it and proceed. What coefficient of vv in the third equation, in place of the present −1-1, would make it impossible to proceed—and force elimination to break down?

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