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Exercise:
Let VW be vector spaces over a field K and let T:Vlongrightarrow W be a linear map. Then: abcliste abc forall nin mathbbN a_...a_nin K v_...v_nin V we have Tleft _i^n a_iv_iright_i^n a_iTv_i abc T_V_W abcliste

Solution:
Proof. abcliste abc Follows from the definition of a linear map combined with induction on n. abc _W T_V-T_VT_V-_VT_V. abcliste
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Exercise:
Let VW be vector spaces over a field K and let T:Vlongrightarrow W be a linear map. Then: abcliste abc forall nin mathbbN a_...a_nin K v_...v_nin V we have Tleft _i^n a_iv_iright_i^n a_iTv_i abc T_V_W abcliste

Solution:
Proof. abcliste abc Follows from the definition of a linear map combined with induction on n. abc _W T_V-T_VT_V-_VT_V. abcliste
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Tags
eth, hs22, linear map, lineare algebra, proof, vector space
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Difficulty
(3, default)
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0 (default)
Language
ENG (English)
Type
Proof
Creator rk
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