A First Course in Linear Algebra · Problem C24

Systems of Linear Equations — Robert Beezer

Mathematics — Linear Algebra · solve-linear-system-solution-set

Problem

Find the solution set of the system of linear equations. Give the values of

n

and

r

, and interpret your answers in light of the theorems of this section.

\begin{aligned} x_1 - 2x_2 + x_3 - x_4 &= 2\\ x_1 + x_2 + x_3 - x_4 &= 2\\ x_1 \phantom{{}+x_2} + x_3 - x_4 &= 2 \end{aligned}