exo7 3398

Inverser les matrices suivantes :

1

\(\begin{pmatrix}0 & &(1) \cr &\ddots \cr (1)& &0 \cr\end{pmatrix}\).

2

\(\begin{pmatrix}a & &(b) \cr &\ddots \cr (b)& &a \cr\end{pmatrix}\).

3

\(\begin{pmatrix} 1 &1 & &(0) \cr &\ddots &\ddots \cr & &\ddots &1 \cr \span(0) & &1 \cr\end{pmatrix}\).

4

\(\begin{pmatrix} 1 &\bar\alpha &\bar\alpha^2 \cr \alpha &1 &\bar\alpha \cr \alpha^2 &\alpha &1 \cr \end{pmatrix}\), \(\alpha \in \C\).

5

\(\begin{pmatrix} (0) &&a_n \cr &\cdots\cr a_1 &&(0) \cr\end{pmatrix}\).

6

\(\begin{pmatrix} 1+\frac 1{\lambda_1} &&(1) \cr &\ddots \cr (1) & &1+\frac 1{\lambda_n} \cr \end{pmatrix}\).