A First Course in Linear Algebra · Problem C17

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+5x2=−8−2x1+5x2+5x3+2x4=9−3x1−x2+3x3+x4=37x1+6x2+5x3+x4=30\begin{aligned} -x_1 + 5x_2 &= -8\\ -2x_1 + 5x_2 + 5x_3 + 2x_4 &= 9\\ -3x_1 - x_2 + 3x_3 + x_4 &= 3\\ 7x_1 + 6x_2 + 5x_3 + x_4 &= 30 \end{aligned}

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