Question

Bestimmen Sie nachvollziehbar das Inverse der Matrix A = \( \begin{pmatrix} 1 & 1 & 1 \\ -1 & 1 & -3 \\ 0&2&-5 \end{pmatrix} \)

Answer 1

[1, 1, 1, 1, 0, 0]
[-1, 1, -3, 0, 1, 0]
[0, 2, -5, 0, 0, 1]

II + I

[1, 1, 1, 1, 0, 0]
[0, 2, -2, 1, 1, 0]
[0, 2, -5, 0, 0, 1]

III - II

[1, 1, 1, 1, 0, 0]
[0, 2, -2, 1, 1, 0]
[0, 0, -3, -1, -1, 1]

3*I + III ; 3*II - 2*III

[3, 3, 0, 2, -1, 1]
[0, 6, 0, 5, 5, -2]
[0, 0, -3, -1, -1, 1]

2*I - II

[6, 0, 0, -1, -7, 4]
[0, 6, 0, 5, 5, -2]
[0, 0, -3, -1, -1, 1]

Normieren

[1, 0, 0, - 1/6, - 7/6, 2/3]
[0, 1, 0, 5/6, 5/6, - 1/3]
[0, 0, 1, 1/3, 1/3, - 1/3]