Question

By justifying your answer, determine whether the function 〈,〉 defines an inner product on V.

(a) 〈(u1,u2,u3,u4),(v1,v2,v3,v4)〉=u1v4−5u2v3〈V=R4.

(b) 〈(u1,u2),(v1,v2)〉=2–√u1v1+u2v2 V=R2.

Please solve it in very detail, and make sure it is correct.

Answer 1

ca) o < (4, 42, 43, 4a), (44, 44, 45, 0+)> be cause = 4,V4 - 5 U₂ V3 it is not an inner product space it does not Symmetrie W = (M1, Ue, üg, 44) V = (04, 4s, ls, lla) <x,y)= 4 4-5 uz Uz & TY,x) = 444 -5443 it may be equal o put X=(1,0,0,2) Y = (1,0,0, 4) Thank x, y)=4 TY,X7 on may not = 2

os 2 if < (4,4), (1, 2)>=2-J44, +421 VEIR it is an inner product space it is hald be forklowing your properties <x,y> 20 o & X, YER² but it is foute failed Cef X= (2,4) Y= (4/4) Then <x,y) = (2, 2), (4,4) =d-12x4+2x4 = 2-16 = 2-4= Thus this is is not negetive IS not Thes this imer product Space -2 TO non 1 a