By justifying your answer, determine whether the function (, ) defines an inner product on V....
By justifying your answer, determine whether the function 〈,〉〈,〉 defines an inner product on VV. (a) 〈(u1,u2,u3,u4),(v1,v2,v3,v4)〉=u1v4−5u2v3〈(u1,u2,u3,u4),(v1,v2,v3,v4)〉=u1v4−5u2v3 and V=R4V=R4. (b) 〈(u1,u2),(v1,v2)〉=2–√u1v1+u2v2〈(u1,u2),(v1,v2)〉=2u1v1+u2v2 and V=R2V=R2.
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.
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,...
The function, By justifying your answer, determine whether 7 defines an loner Product cas (cui nas Ws, un, (wu. Var Vauva) ) - Li. Wy - 5w, vg and Va " (b) Kuus), u. Nad >=V7 Live + us to and V=R*
Problem #3: Let R4 have the inner product <u, v> = ulv1 + 2u2v2 + 3u3v3 + 40404 (a) Let w = (0,9,5,-2). Find llwll. (b) Let W be the subspace spanned by the vectors U1 = = (0,0, 2, 1), and u2 = (-3,0,–2, 1). Use the Gram-Schmidt process to transform the basis {uj, u2} into an orthonormal basis {V1, V2}. Enter the components of the vector v2 into the answer box below, separated with commas.
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
(1 point) Let {uj, u2, u2 ) be an orthonormal basis for an inner product space V. Suppose y = qui + buz + cuz is so that|lvl1 = V116. (v, uz) = 10, and (v. uz) = 4. Find the possible values for a, b, and c. a = CE (1 point) Suppose U1, U2, Uz is an orthogonal set of vectors in Rº. Let w be a vector in Span(v1, 02, 03) such that UjUi = 42, 02.02...
Let v1,v2,v3 and v4 be linearly independent vectors in R4.
Determine whether each set of vectors is linearly independent or
dependent. Please solve d) and f)
U1, 2, 03, 4
2. Suppose that V is an inner product space. (i) Prove that, for any vectors 01, 02 € V, || 0111? + || 0,2||2 = || v1 + v2||2 + || 01 – v2||2 2 (ii) Prove that, for any vectors V1, V2 € V, if v, and v, are orthogonal then || 01 || + || 112 || 2 = || 01 + 02||2.
3. Let V be a finite dimensional inner product space, and suppose that T is a linear operator on this space. (i) Let B be an ordered orthonormal basis for V and let U be the linear operator on V determined by [U19 = (T);. Then, for all 01,09 € V, (01, T(02)) = (U(V1), v2) (ii) Prove that the conclusion of the previous part does not hold, in general, if the basis 8 is not orthonormal.