A First Course in Linear Algebra · Problem C11

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. 3x1+4x2−x3+2x4=6x1−2x2+3x3+x4=210x2−10x3−x4=1\begin{aligned} 3x_1 + 4x_2 - x_3 + 2x_4 &= 6\\ x_1 - 2x_2 + 3x_3 + x_4 &= 2\\ 10x_2 - 10x_3 - x_4 &= 1 \end{aligned}

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