Linear Algebra and Its Applications · Problem 1.2.8

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · geometry-of-linear-equations

Problem

Explain why the system u+v+w=2u+2v+3w=1v+2w=0\begin{aligned} u + v + w &= 2 \\ u + 2v + 3w &= 1 \\ v + 2w &= 0 \end{aligned} is singular by finding a combination of the three equations that adds up to 0=10 = 1. What value should replace the last zero on the right side to allow the equations to have solutions—and what is one of the solutions?

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