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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′.
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