Problem #8: Use least squares to find the orthogonal projection of u onto the subspace of Rª spanned by the vectors V₁, V2, andV3, whereProblem #8:u = (0, 3, 2, 0), V₁ = (8, 0, 0, 1), v2 = (0, 1, -1, 0), v3 = (1, 1, 0, -8).Enter your answer symbolically,as in these examplesEnter the four components,separated with commas.

Answered: Image /qna-images/answer/4c1627ab-a844-4d4c-8db3-f18e86b0b43a.jpg

Answered: Problem #8: Use least squares to find…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Given the set of vectors under R4: V₁ = V3 = 2, 0, 0,2 > 3,3,5,5> V4 = Find the dimension of the subspace W of V = R4 spanned by the vectors (V₁, V₂, V3, V4}. RREF solution can be done via MATLAB, but state the basis of your conclusion. What are the basis vectors for the subspace? Given the set of vectors under P3 P₁ = 1+ 2x + 3x² + 4x³ P₂ = x + 2x² + 3x³ P3 = x² + 2x³ P4 = x³ Find the dimension of the subspace W of V = P3 spanned by the vectors {P₁, P2, P3, P4}. RREF solution can be done via MATLAB, but state the basis of your conclusion. Are the set of vectors a basis for P3? If not, state the basis vectors that forms a basis for the subspace? Find a basis for R³ that includes the vectors and Solution: Basis Vectors
4] Show that the following sets of vectors are linearly dependent in R3. (c) {{5, 2, -3), (3, 0, 4), (-3, 0, -4)} (d) {{1, 1, 1), (2, 2, 2), (0, 1, 5)}
I.1. Find the adjoint of the matrix,then use the adjoint to find the inverse if possible 2.Find the Equation of (-4,0) and (4,4)3. Find the volume of the tetrahedron (2,0,0), (0,2,0), and (2,2,2).II.4. Determine whether the set of W is a subspace of R^3 with the standard operation. Justify your answer. a. b.5. Determine whether the set S is linearly independent or linearly dependent.a.b.c.
Given the set of vectors under P3 P₁ = 1+ 2x + 3x² + 4x³ P₂ = x + 2x² + 3x³ P3 = x² + 2x³ P₁ = x³ Find the dimension of the subspace W of V = P3 spanned by the vectors {P₁, P2, P3, P4}. RREF solution can be done via MATLAB, but state the basis of your conclusion. Are the set of vectors a basis for P3? If not, state the basis vectors that forms a basis for the subspace? nd Basis Vectors
please help
Please don't solve it by handwritten
I know the basis converted to orthogonal is {<2, 1, -1, 1>,<11, -12, 5, -5>,<-1, -3, 0, 5>} and that the magnitude of these will be sqrt(7), sqrt(315), sqrt(35) - but I'm not sure how to use these to convert the basis to orthonormal.
Find the decomposition a = a|| + a₁ with respect to b if a = (3, 4, 2), b = (3, 4, 6). = (a||x, a||y, a||z) a¹b = (alx, aly, alz) (Enter the components of vectors using symbolic notation and fractions where needed.) a||x ally a||z ab = = = alx = aly = alz =
Solve all quation
1- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (-3,0,4), (5,-1,2), (1,1,3) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³ 2- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthonormal basis for R³, then obtain an orthonormal basis from them. Express (3,7,-4) as a linear combination of the orthonormal basis. 3- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (1,1,0), (0,0,1), (0,1,1) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³ 4- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthogonal basis for R³, then obtain an orthonormal basis from them. Express (2,3,-4) as a linear combination of the orthonormal basis. 5- Find the coordinates of the vector u = (0,25, 1) with respect to the orthogonal basis v₁ = ( 3,4,0), V₂ = (−4, 3, 0 ) and v₂ = (−4,3,0) 6- Find the coordinates of the vector U = (7,5,2) with respect to the basis V₁ =…
6. (a) Determine whether the set of all vectors of the form (a,b,c), where b = %3D a+c, is a subspace of R³.
What is the matrix P = (P₁) for the projection of R³ onto the subspace V spanned by the vectors 23 a2 -D-D = -2? -1.5

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