Exercise 1.3.5 For each of the following homogeneous systems, find a set of basic solutions and express the gen- eral solution as a linear combination of these basic solu- tions. a. b. - x1 + 2x2 x3 + 2x4+x5=0 x1 + 2x2 + 2x3 +x5=0 2x1 + 4x2 - 2x3 + 3x4+x5=0 - x1 + 2x2 xX3+x4+ x5 = 0 -x1-2x2+2x3 + x5=0 -x1-2x2+3x3 + x4+3x5=0 c. - x1 + x2 x3 + 2x4 + x5 = 0 x5=0 x5 = 0 x1 + 2x2 x3 + x4+ - 2x13x2 x3+2x4 + x5=0 - 4x15x22x3 +5x4+2x5 = 0

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