Berechne die Inverse der Matrix

Question

9 -1 0 0

0 8 -2 0

0 0 7 -3

0 0 0 6

Bin soweit gekommen, aber jetzt steh ich an...wie würdet ihr an die Sache rangehen?

Answer 1

[9, -1, 0, 0, 1, 0, 0, 0]
[0, 8, -2, 0, 0, 1, 0, 0]
[0, 0, 7, -3, 0, 0, 1, 0]
[0, 0, 0, 6, 0, 0, 0, 1]

2*III + IV

[9, -1, 0, 0, 1, 0, 0, 0]
[0, 8, -2, 0, 0, 1, 0, 0]
[0, 0, 14, 0, 0, 0, 2, 1]
[0, 0, 0, 6, 0, 0, 0, 1]

7*II + III

[9, -1, 0, 0, 1, 0, 0, 0]
[0, 56, 0, 0, 0, 7, 2, 1]
[0, 0, 14, 0, 0, 0, 2, 1]
[0, 0, 0, 6, 0, 0, 0, 1]

56*I + II

[504, 0, 0, 0, 56, 7, 2, 1]
[0, 56, 0, 0, 0, 7, 2, 1]
[0, 0, 14, 0, 0, 0, 2, 1]
[0, 0, 0, 6, 0, 0, 0, 1]

Normieren

[1, 0, 0, 0, 1/9, 1/72, 1/252, 1/504]
[0, 1, 0, 0, 0, 1/8, 1/28, 1/56]
[0, 0, 1, 0, 0, 0, 1/7, 1/14]
[0, 0, 0, 1, 0, 0, 0, 1/6]