Elementary Linear algebra
Chapter 1.2
Exercise 3
By allotting the arbitrary value s for free variable x4​, the general solution is given by the formulas
x1​=13s−10, x2​=13s−5, x3​=2−s, x4​=s.
Substituting x3​=−4−3x5​ into the second equation yields
x1​x3​x4​​=−11−7x2​+2x5​=−4−3x5​=9−3x5​​
By allotting the arbitrary values s for free variable x5​ and t for variable x2​, the general solution is given by the formulas
x1​=−11−7t+2s, x2​=t, x3​=−4−3s, x4​=9−3s, x5​=s.
Answer
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