POMOGITE POJALUYSTA RESHIT ZADANIE PO ALGEBRE NA ANGLIYSKOM YAZIKE

Question

SUPPOSE THAT THE DOT PRODUCT OF U =[U1,U2] AND V=[V1,V2] WHERE DEFINED AS U*V =5U1V1+2U2V2. WHICH (IF ANY) OF THE FOLLOWING STATEMENTS WOULD BE TRUE FOR ALL VECTORS U,V,W AND ALL SCALARS C ?
a. U * V = V * U 
b. U *(V + W) = U * V + U * W
c. (CU) * V = C (U * V)

Ирина Кох(Волкова) · Accepted Answer

а) U*V=5U1V1+2U2V2; V*U=5V1U1+2V2U2 = 5U1V1+2U2V2 => U*V=V*U - true
б) U*(V+W) = 5U1(V1+W1)+2U2(V2+W2)=5U1V1+5U1W1+2U2V2+2U2W2= 5U1V1+2U2V2+5U1W1+ 2U2W2=U*V+U*W - true
в) (CU)*V=5CU1V1+2CU2V2=C(5U1V1+2U2V2) = C(U*V) - true