A First Course in Linear Algebra · Problem C13

Systems of Linear Equations — Robert Beezer

Mathematics — Linear Algebra · solve-linear-system-rref-computer

Problem

Find all solutions to the system of linear equations. Use your favorite computing device to row-reduce the augmented matrices for the systems, and write the solutions as a set, using correct set notation. x1+2x2+8x3−7x4=−23x1+2x2+12x3−5x4=6−x1+x2+x3−5x4=−10\begin{aligned} x_1 + 2x_2 + 8x_3 - 7x_4 &= -2\\ 3x_1 + 2x_2 + 12x_3 - 5x_4 &= 6\\ -x_1 + x_2 + x_3 - 5x_4 &= -10 \end{aligned}

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