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E is a vectorial plane. his base is
B=(i→,j→). f is an endomorphism
and his matrix in base B is M=matrix (((1 2)),((1 0))).
The applications g and h are also
endomorphisms of E defined by:
g=f+Id_E and h=f−2Id_E.
1) Determinate the matrix of g and
h in base B.
2) Determinate ker g and give one base e_1→.
3)Determinate ker h and give one base e_2.→
4) Demonstrate that B′=(e_1→,e_2→) is
a base of E, then determinate the
matrix of f in B′.