Consider the inner product space 1 Cr-1,1] with inner product: | f(x)g(x)dx %3D -1 Let U= x form a basis for a subspace of C 1. Show that U is an orthonormal basis. 2. Find the best least squares approximation to h(x) =x +x by a lin

Q: An inner product and an associated norm are defined on R² by the weighted scalar product where u =…

A:

Q: 4. Consider the subspace V of R' given by 3 V = span (a) Find an orthonormal basis for the…

A: vector subspace  V  of  ℝ4  given by ,               V = span 1001 , 31-11 (.)  If  W be a subspace…

Q: *1. Which of the following are subspaces? Justify your answer in each case. (d) (x € R³ : x² + x² +…

A:

Q: Show that any isometry of R^n which fixes the origin is linear, and hence must be of the form f(x) =…

A: Introduction A square matrix is said to be an orthogonal matrix if…

Q: Let u = (18,1,0). Find the orthogonal projection of u onto the subspace W spanned by the…

A:

Q: Consider the following vectors! x₁ = x2= 6 x3 =1 16 -5 X=[²] { Ⓒ) are the weckers S [ X₁, X₁, X3z…

A:

Q: 4. Find an orthonormal basis for W+, where W is the subspace of R' spanned by the vectors (-1,…

A: To find- Find an orthonormal basis for W⊥, where W is the subspace of ℝ4 spanned by the vectors -1,…

Q: (a) Find orthonormal vectors 91, 92, 93 such that 91, 92 span the column space of 1 2 1 A - 1 -2 4…

A:

Q: 4. (a) Let {b,, b2, b3, bą} be an orthonormal basis for a three-dimensional subspace of Rº, and let…

A: For (a), Note that {b1, b2, b3, b4 } be an orthonormal basis. We are given that u = b1-2b2+b3-2b4…

Q: Let W C R" be a subspace and let W- C R" be its orthogonal complement. Let S = {u1,..., uk} be an…

A:

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213