# Aufgabe 8.1
restart;
with(LinearAlgebra):
v := <3,-4,1>;
w := <2,1,2>;
A := Matrix([[ 1 , 2 , 0 ],
[ 3 , 4 , -2 ],
[ 2 , -1 , 5 ]]);
S := Matrix([[ 2 , 1 , 1 ],
[ 1 , 4 , 1 ],
[ 1 , 1 , 2 ]]);
A . v;
S . A - A . S;
I3 := IdentityMatrix(3);
Determinant(A - 5*I3);
Transpose(w) . S . w;
S^(-1) . A . S; # oder MatrixInverse(S) . A . S;