Exercícios de Álgebra Linear

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Álgebra Linear
Primeira Lista de Exercı́cios
01. Utilizando o método do escalonamento, resolva os sistemas a seguir.
(a)
{
2x1 + x2 = 8
4x1 − 3x2 = 6
(b)
{
2x1 − 3x2 = 5
−4x1 + 6x2 = 8
(c)
{
4x1 + 3x2 = 4
3x1 + 9
4
x2 = 3
(d)

x1 + 2x2 − x3 = 1
2x1 − x2 + x3 = 3
−x1 + 2x2 + 3x3 = 7
(e)

2x1 + x2 + 3x3 = 1
4x1 + 3x2 + 5x3 = 1
6x1 + 5x2 + 5x3 = −3
(f)

3x1 + 2x2 + x3 = 0
−2x1 + x2 − x3 = 2
2x1 − x2 + 2x3 = −1
(g)

1
3
x1 + 2
3
x2 + 2x3 = −1
x1 + 2x2 + 3
2
x3 = 3
2
1
2
x1 + 2x2 + 12
5
x3 = 1
10
(h)

x2 + x3 + x4 = 0
3x1 + 3x3 − 4x4 = 7
x1 + x2 + x3 + 2x4 = 6
2x1 + 3x2 + x3 + 3x4 = 6
(i)

x1 + x2 = 0
2x1 + 3x2 = 0
3x1 − 2x2 = 0
(j)

3x1 + 2x2 − x3 = 4
x1 − 2x2 + 2x3 = 1
11x1 + 2x2 + x3 = 14
(k)

2x1 + 3x2 + x3 = 1
x1 + x2 + x3 = 3
3x1 + 4x2 + 2x3 = 4
(l)

x1 − x2 + 2x3 = 4
2x1 + 3x2 − x3 = 1
7x1 + 3x2 + 4x3 = 7
(m)

x1 + x2 + x3 + x4 = 0
2x1 + 3x2 − x3 − x4 = 2
3x1 + 2x2 + x3 + x4 = 5
3x1 + 6x2 − x3 − x4 = 4
(n)

x1 − 2x2 = 3
2x1 + x2 = 1
−5x1 + 8x2 = 4
(o)

−x1 + 2x2 − x3 = 2
−2x1 + 2x2 + x3 = 4
3x1 + 2x2 + 2x3 = 5
−3x1 + 8x2 + 5x3 = 17
(p)

x1 + 2x2 − 3x3 + x4 = 1
−x1 − x2 + 4x3 − x4 = 6
−2x1 − 4x2 + 7x3 − x4 = 1
(q)

x1 + 3x2 + x3 + x4 = 3
2x1 − 2x2 + x3 + 2x4 = 8
x1 − 5x2 + x4 = 5
(r)

x1 − 3x2 + x3 = 1
2x1 + x2 − x3 = 2
x1 + 4x2 − 2x3 = 1
5x1 − 8x2 + 2x3 = 5