Linear Algebra and Its Applications · Problem 1.3.15

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · gaussian-elimination

Problem

If rows 1 and 2 are the same, how far can you get with elimination (allowing row exchange)? If columns 1 and 2 are the same, which pivot is missing?

\begin{array}{ll} 2x - y + z = 0 & 2x + 2y + z = 0 \\ 2x - y + z = 0 & 4x + 4y + z = 0 \\ 4x + y + z = 2 & 6x + 6y + z = 2. \end{array}