Use Maple or another appropriate software package to solve the systems of equations in Exercises. If you are using Mathematica or MATLAB, see the Technology Resource Manual for appropriate commands. (To become more comfortable with the software package you are using, you may wish to practice using it to solve some of the smaller systems in Exercises 1-16 before doing these.)
62x1 + 82x2 + 26x3 – 4x4 + 32x5 + 34x6 – 2x7 – 4x8 = 0
93x1 + 123x2 + 67x3 – 36x4 + 106x5 + 51x6 + 31x7 – 188x8 = 0
– 589x1 – 779x2 – 303x3 + 647x4 – 330x5 – 323x6 – 256x7 – 246x8 = 0
403x1 + 533x2 + 365x3 – 2493x4 + 263x5 + 50x6 + 981x7 + 1345x8 = 0
2511x1 + 3321x2 + 1711x3 – 2636x4 + 2358x5 + 1357x6 + 1457x7 – 2323x8 = 0
2356x1 + 3116x2 + 2038x3 – 6828x4 + 2418x5 + 1936x6 + 3596x7 – 357x8 = 0
Exercises 1-16
Solve the systems of equations in Exercise.
Exercise 1
x + y – z = 0
2x + 3y – 2z = 6
x + 2y + 2z = 10
Exercise 2
2x + y – 2z = 0
2x – y – 2z = 0
x + 2y – 4z = 0
Exercise 3
2x + 3y – 4z = 3
2x + 3y – 2z = 3
4x + 6y – 2z = 7
Exercise 4
3x + y – 2z = 3
x – 8y – 14z = –14
x + 2y + z = 2
Exercise 5
x + 3z = 0
2x + y – z = 0
4x + y + 5z = 0
Exercise 6
2x + 3y + z = 4
x + 9y – 4z = 2
x – y + 2z = 3
Exercise 7
3x1 + x2 – 3x3 – x4 = 6
x1 + x2 – 2x3 + x4 = 0
3x1 + 2x2 – 4x3 + x4 = 5
x1 + 2 x2 – 3x3 + 3x4 = 4
Exercise 8
x1 + x2 – x3 + 2x4 = 1
x1 + x2 – x3 – x4 = –1
x1 + 2x2 + x3 + 2x4 = –1
2x1 + 2x2 + x3 + x4 = 2
Exercise 9
x1 + 2x2 – 3x3 + 4x4 = 2
2x1 – 4x2 + 6x3 – 5x4 = 10
x1 – 6x2 + 9x3 – 9x4 = 8
3x1 – 2x2 + 4x3 – x4 = 12
Exercise 10
x1 – x2 + x3 + x4 – x5 = 0
2x1 – x2 + 2x3 – x4 + 3x5 = 0
2x1 – x2 – 2x4 + x5 = 0
x1 + x2 – x3 – x4 + 2x5 = 0
2x1 + 4x3 + x4 + 3x5 = 0
Exercise 11
x + 2y + z = –2
2x + 2y – 2z = 3
Exercise 12
2x – 4y + 6z = 2
–3x + 6y – 9z = 3
Exercise 13
x – 2y = 2
x + 8y = –4
2x + y = 1
Exercise 14
2x + 3y = 5
2x + y = 2
x – 2y = 1
Exercise 15
2x1 – x2 – x3 + x4 + x5 = 0
x1 – x2 + x3 + 2x4 – 3x5 = 0
3x1 – 2x2 – x3 – x4 + 2x5 = 0
Exercise 16
x1 – 3x2 + x3 – x4 – x5 = 1
2x1 + x2 – x3 + 2x4 + x5 = 2
–x1 + 3x2 – x3 – 2x4 – x5 = 3
2x1 + x2 – x3 – x4 – x5 = 6
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