*Znajdź kombinacje wektorów (1,2,3)(2,1,1)(3,0,1) ze współczynnikami 2,1,0: 2(1,2,3)+1(2,1,1)+0(3,0,1)=(4,5,7)

Przekształcenia liniowe: 1) f(v₁+v₂)=f(v₁)+f(v₂) || 2) f(k*f)=k*f(v) |||| 1)F(f₁+f₂)=(f₁+f₂)'=F(f₁)+F(f₂) ||

2) F(k*f)=(kf)'=kF(f)

Z.1 k(f)=f² || k(2f)=2²*f²=4k(f)
Z.2 L(f)=f+1 || L(0+0)=0+1 || L(0)+L(0)=(0+1)+(0+1)=2
Z.3 G(f)(x)=f(x)+f(x-1) || 1) G(f₁+f₂)(x)=(f₁+f₂)(x)+(f₁+f₂)(x-1)=f₁(x)+f₂(x)+f₁(x-1)+f₂(x-1) ||

(G(f₁)+G(f₂))(x)=G(f₁)(x)+G(f₂)(x)=f₁(x)+f₁(x-1)+f₂(x)+f₂(x-1) || 2) G(kf)(x)=kf(x)+kf(x-1)=

k(f(x)+f(x-1))=k*G(f)(x)

Z.4 1) fog(v₁+v₂)=f(g(v₁+v₂))=f(g(v₁)+(g(v₂))=f(g(v₁))+f(g(v₂)) || 2) f(g(kv))=f(kg(v))=kf(g(v))

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