Linear Algebra and Its Applications · Problem 1.2.4

Matrices and Gaussian Elimination — Gilbert Strang

Mathematics · geometry-of-linear-equations

Problem

Sketch these three lines and decide if the equations are solvable: 3 by 2 systemx+2y=2x−y=2y=1.\textbf{3 by 2 system} \quad \begin{aligned} x + 2y &= 2 \\ x - y &= 2 \\ y &= 1. \end{aligned} What happens if all right-hand sides are zero? Is there any nonzero choice of right-hand sides that allows the three lines to intersect at the same point?

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