Question

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

C Max R x 146 Per xC cel x C G C G X Cxc Mix CCXO Pux app.crcaiak.com/tudent/assets/math-2203-77-linal-exam-2020 Q8 (8 points) By justifying your answer, determine whether the function (,) defines an inner product on V. My Courses (a) ((U1, U2, U3, U1), (V1, V2, V3, V4)) = U1V1 – 54203 and V = R4 Linear Algebra II (MATH-2203-7... Applied Math for Business and ... (b) ((U1, 42), (V1, V2)) = V2 4101 + U2v2 and V =R2 Time left Show + Drag and drop your files or cl browse... Type here to search 1 e 4 ENG 306 PM 2020-37-30

Answer 1

(14,42,43,44), (V, V2, 33, 4) = 4,44543 and V=R4 here, the function > is not an inner product it does not satisfy the non-negativity axion <ũ, q>>0 Example: Let u = 14,42,"3,44) =(!!!!!) then, cū ü> = 4,44-54243 - OV - 500 =1-5=-40 An inner product on a vector space V is a function that associates a real number 5, %> with each pair of vectors ū and I, and satisfies the following axioms. U) <ü, >< a> Gi) <utw) =<ūv>+<uw) i) <09, >z<<ū> Liv> <qu>20 and <a.u>zo ūzö . The given function is not an inner product. _b) <(",,4), (V, W) and V=1R² (1 het u =(4,42), Ñ = (V, V, Then, Lū, j) = 524, 4, +424 =5244, +Y"2 {": ab=ba for all aber = <% ū> iku,w>=<, ü> ii) Let u = 84,42), W = cry), w = (W,W2) then w tw = (1, 2)+(W,,w2} = (Y+W,,"+W2) Now, <u, Ñ tw) - 124,(4,+W,) + 4₂ (Y + wy) = 524 4+ [2 4 W, tyktų uz =($24, Y+4K) + ({24 W, tYWZ) =cG,u>+<ü,m> ico, Ñ tw>=<ūv>+ <uw> iii) het Cer; they cũ = c(4,2)=(K4, C4) :(05, ū>= 5(24) +(64) ų = c(B4Y) + ((Yų ac {24, Y + 4₂ V ₂) = coû.j} (chw>=2<ü.v> (iv) <u, ū>= 524, 4, +4₂" and Lü, ü>=0 - 524² +42=0 in the given tunction is an inner product