(a) Find an orthonormal basis for the linear subspace V of R4 generated by the vectors 1 1 1 1 2 (b) What is the projection of the vector on the linear subspace V?
Find the projection of the vector v onto the subspace S. 0 -1 -1 1 S = span V = 0 0 1 1 projs v = JOLI
2) The vector is in the subspace H with a basis B = {1,5}. Find the B-coordinate vector of 3 5x = [-2], 62 = (-). =) Answer:
Problem 4 Let W a subspace of R4 with a set of basis: 1 [01 [2] 0 11 lo lo] Li Find and orthonormal basis for W! Problem 4 Let W a subspace of R4 with a set of basis: 1 [01 [2] 0 11 lo lo] Li Find and orthonormal basis for W!
1 The vector V1 = -8 spans a subspace V of the indicated Euclidean space. Find a basis for the orthogonal complement v of V. 4 Select the correct choice below and, if necessary, fill in the answer box within your choice. OA Evt A basis for the orthogonal complement is { {} (Use a comma to separate vectors as needed.) There is no basis for the orthogonal complement v. OB.
(6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y +3z 0. Let L be the set of solutions of the inhomogeneous linear equation (a) Define affine subspace of a vector space. (b) Prove that L is an affine subspace of R3 (c) Compute a vector v such that L = v + W (6) In R3, let W be the set of solutions of the homogeneous linear equation r + 2y...
Determine if the set V = {at? | a € R} is a subspace of the vector space P2 = {ao +ajt + azt? | ao, a1, az ER}. You may assume that vector addition in P2 is given by the usual addition of polynomials and that the scalars used in scalar multiplication are real numbers. If you decide that Vis a subspace of P2, then identify the zero vector in V and explain briefly why Vis closed under vector...
Problem 9. Let V be a vector space over a field F (a) The empty set is a subset of V. Is a subspace of V? Is linearly dependent or independent? Prove your claims. (b) Prove that the set Z O is a subspace of V. Find a basis for Z and the dimension of Z (c) Prove that there is a unique linear map T: Z → Z. Find the matrix representing this linear map and the determinant of...
6. Find a basis for the subspace W= {xeR* | x1 +x2 +xy + x4 = 0, x2 +x4 = 0 } and determine its dimension: 4. Prove or disprove: A set with only one vector in it is linearly independent
(1 point) Determine whether the given set S is a subspace of the vector space V. A. V = R", and S is the set of solutions to the homogeneous linear system Ax = 0 where A is a fixed mxn matrix. B. V is the vector space of all real-valued functions defined on the interval (-oo, oo), and S is the subset of V consisting of those functions satisfying f(0) 0 C. V Mn (R), and S is the...