Question

In: Math

Using least squares, find the orthogonal projection of u onto the subspace of R4 spanned by...

Using least squares, find the orthogonal projection of u onto the subspace of R4 spanned by the vectors v1, v2, and v3, where

u  =  (6, 3, 9, 6), v1  =  (2, 1, 1, 1), v2  =  (1, 0, 1 ,1), v3  =  (-2, -1, 0, -1).

Solutions

Expert Solution

Hope this helps!!


Related Solutions

2a. Find the orthogonal projection of [9,40,-29,4] onto the subspace of R4 spanned by [1,6,5,6] and...
2a. Find the orthogonal projection of [9,40,-29,4] onto the subspace of R4 spanned by [1,6,5,6] and [5,1,5,5]. Answer choices: [2,14,-15,7] [-32,13,-10,7] [0,9,12,6] [-5,-2,3,2] [-12,0,-9,-9] [-16,20,0,4] [27,29,29,21] [-3,1,2,7] [-23,7,-3,-9] [-15,5,-15,30] 2b. Find the orthogonal projection of [17,18,-10,24] onto the subspace of R4 spanned by [2,7,1,6] and [3,7,3,4]. Answer choices: [-34,-22,-29,-34] [-6,4,-2,0] [-12,36,21,33] [3,21,-3,24] [7,-14,-12,1] [5,3,32,45] [14,32,12,11] [9,13,18,11] [20,2,-3,19] [-2,-6,1,-7]
Let W be a subspace of R^n, and P the orthogonal projection onto W. Then Ker...
Let W be a subspace of R^n, and P the orthogonal projection onto W. Then Ker P is W^perp.
Prove that the solution of the discrete least squares problem is given by the orthogonal projection.
Prove that the solution of the discrete least squares problem is given by the orthogonal projection.
Find a basis for the subspace of R4 spanned by (1,0,-2,1), (2,-1,2,1), (1,1,1,1), (0,1,0,1), (0,1,1,0) containing...
Find a basis for the subspace of R4 spanned by (1,0,-2,1), (2,-1,2,1), (1,1,1,1), (0,1,0,1), (0,1,1,0) containing the first and fifth vectors
determine the orthogonal bases for subspace of C^3 spanned by the given set of vectors. make...
determine the orthogonal bases for subspace of C^3 spanned by the given set of vectors. make sure that you use the appropriate inner product of C^3 A=[(1+i,i,2-i),(1+2i,1-i,i)
There are three vectors in R4 that are linearly independent but not orthogonal: u = (3,...
There are three vectors in R4 that are linearly independent but not orthogonal: u = (3, -1, 2, 4), v = (-2, 7, 3, 1), and w = (-3, 2, 4, 11). Let W = span {u, v, w}. In addition, vector b = (2, 1, 5, 4) is not in the span of the vectors. Compute the orthogonal projection bˆ of b onto the subspace W in two ways: (1) using the basis {u, v, w} for W, and...
Problem 4. Let P be the orthogonal projection associated with a closed subspace S in a...
Problem 4. Let P be the orthogonal projection associated with a closed subspace S in a Hilbert space H, that is P is a linear operator such that P(f) = f if f ∈ S and P(f) = 0 if f ∈ S⊥. (a) Show that P2 = P and P∗ = P. (b) Conversely, if P is any bounded operator satisfying P2 = P and P∗ = P, prove that P is the orthogonal projection for some closed subspace...
Check the true statements below: A. The orthogonal projection of y onto v is the same...
Check the true statements below: A. The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cv whenever c≠0. B. If the columns of an m×n matrix A are orthonormal, then the linear mapping x→Ax preserves lengths. C. If a set S={u1,...,up} has the property that ui⋅uj=0 whenever i≠j, then S is an orthonormal set. D. Not every orthogonal set in Rn is a linearly independent set. E. An orthogonal matrix is invertible.
(a) Find the matrix representation for the orthogonal projection Pr : R 4 → R 4...
(a) Find the matrix representation for the orthogonal projection Pr : R 4 → R 4 onto the plane P= span 1 -1 -1 1 -1 -1 1 1 (b) Find the distance of vector ~y = 2 0 0 4 from the plane P.
find the projection vector of the vector v = (2,3,5) onto the plane z = 2x...
find the projection vector of the vector v = (2,3,5) onto the plane z = 2x + 3y -1
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT