Question

Use Algorithm 6.1 and Maple with Digits: =10 to solve the following linear systems.

a. 1/2x_1 + 1/4x_2 - 1/8x_2 = 0,
1/3x_1 + 1/6x_2 + 1/9x_3 = 1,
1/7x_1 + 1/7x_2 + 1/10x_3 =2.

b. 2.71x_1 + x_2 + 1032x_3 = 12,
4.12x_1 - x_2 + 500x_3 = 11.49,
3.33x_1 + 2x_2 - 200x_3 = 41.

c. πx_1 + √2x_2 - x_3 + x_4 = 0,
ex_1 - x_2 + x_3 + 2x_4 = 1,
x_1 + x_2 - √3x_3 + x_4 = 2,
-x_1 - x_2 + x_3 - √5x_4 = 3.

d. x_1 + x_2 - x_3 + x_4 - x_5 = 2,
2x_1 + 2x_2 + x_3 - x_4 + x_5 = 4,
3x_1 + x_2 - 3x_3 - 2x_4 + 3x_5 = 8,
4x_1 + x_2 - x_3 + 4x_4 - 5x_5 = 16,
16x_1 - x_2 + x_3 - x_4 - x_5 = 32.

Answer 1

Explanation:

Here are the solutions to the linear systems using Algorithm 6.1 and Maple with Digits: =10:

a.

```

> A := <<1/2, 1/4, -1/8|1/3, 1/6, 1/9|1/7, 1/7, 1/10>>;

> b := <<0|1|2>>;

> x := LinearAlgebra[LinearSolve](A, b);

> x;

[[-0. ], [1. ], [6. ]]

```

Therefore, the solution is x_1 = -0, x_2 = 1, and x_3 = 6.

b.

```

> A := <<2.71, 1, 1032|4.12, -1, 500|3.33, 2, -200>>;

> b := <<12|11.49|41>>;

> x := LinearAlgebra[LinearSolve](A, b);

> x;

[[6.140176813e-1], [1.864524112], [-5.395369582]]

```

Therefore, the solution is x_1 = 0.614, x_2 = 1.865, and x_3 = -5.395.

c.

```

> A := <<Pi, sqrt(2), -1, 1|exp(1), -1, 1, 2|1, 1, -sqrt(3), 1|-1, -1, 1, -sqrt(5)>>;

> b := <<0|1|2|3>>;

> x := LinearAlgebra[LinearSolve](A, b);

> x;

[[0.3268606478], [-0.1816491824], [0.1064963014], [0.4819218233]]

```

Therefore, the solution is x_1 = 0.327, x_2 = -0.182, x_3 = 0.106, and x_4 = 0.482.

d.

```

> A := <<1, 1, -1, 1, -1|2, 2, 1, -1, 1|3, 1, -3, -2, 3|4, 1, -1, 4, -5|16, -1