Let V be a real vector space with basis v₁, v2. Define , where A = (043) = [₁ 2] ₁ Assuming that this makes V,. into an inner product space, find an orthonormal basis w₁, W₂ with respect to this inner product in terms of V₁, V2. Vi • Vj = Ajj,' Select one: ○ w₁ = v₁/√√5, W2 = (v₁ – 5v₂)/√/45 W₁ = (v₁ + 2v₂)/√√5, W₂ = (v₁ − v₂)/√√/2 None of the others apply The associated quadratic form q(v) = v - v for the stated dot product is not in fact positive definite, hence there is no orthonormal basis in this case. w₁ = (√5v₁ + √2v2)/√√7, w2 = (-v1 - v₂)/√√/2

Q: = Consider two bases B = {u₁, u₂} and B' = {V₁, V₂} for a certain vector space V. Assume that u₁ =…

A:

Q: Let V be a vector space, let c be a scalar and let u, v, w be vectors in V and ca scalar. Which of…

A:

Q: Express the vector below in Cartesian coordinate: B = 2r sin cosc a₁ + r cose cose aer sind a ax=…

A: Given: The vector, B=2rsinθcosφar+rcosθcosφaθ-rsinφaφ   To express: The given vector in cartesian…

Q: (a) Give examples of three distinct vectors v1, v2, v3 in the vector space R3 such that v2 E…

A: Let v1 = {1,1,1}v2 = {2,3,4}v3 = {1,2,3} Here v2 = {2,3,4} = {1,1,1}+{1,2,3} = v1+v3

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

A:

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: Find a non-zero vector that is orthogonal to (-7,6,5).   Separate your entries by commas, and…

A:

Q: Let ū = (4, –2), ū = (-2,0), and w = (2, 2). Find the vector x that satisfies Tu – u +x = 5x + w. In…

A: Given Let Plugging the values in the equation:

Q: -9 -10 12 -15 A = 4 -8 6. Find a non-zero vector in the column space of A. 69

A:

Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: W4 Pick any vector space V that you want, as long as dim(V) ≥ 6. Then, pick 4 vectors in the space,…

A:

Q: Find orthonormal vectors 91 92 93 in the plane spanned by u = 32 -2,v= 22 2 and w== 973

A: The given vectors, u=32-222, v=-1-441-4, w=-3-273-2. We have to find the orthonormal vectors q1, q2,…

Q: Suppose v1, v2, v3 is an orthogonal set of vectors in R°. Let w be a vector in Span(v1, v2, v3) such…

A:

Q: For vectors, v0= (0,3,4,2),v1= (1,1,2,1), v2= (1,0,0,0), v3= (0,0,1,0), find an orthonormal basis,…

A: Solution by using Gram Schmidt process as follows :

Q: sider the ordered bases B= ((4, –9), (–3,7)) and C = ((4,3), (–2,4)) for the vector space R’ %3D

A:

Q: Let y = *₁ = 0 and ū= 6 . Write y as the sum of two orthogonal vectors, ₁ in Span{u} and 2…

A: Given that the vectors  y→=0-1-2   and  u→=56-1   .

Q: Show that the vector space P, has the basis S = {1, x, x², x³}. %D

A: We have to solve given problem:

Q: Represent the vector ⟨16,8,−14⟩ in terms of the ordered basis B={⟨5,−2,−2⟩,⟨1,−4,2⟩,⟨−1,−5,3⟩}.

A: