5. Let V = R³ and let (-, ) be the standard dot prod-uct.(a) Calculate (3e, + 2e, – €3, 2e2 + 4e3).-(b) Let W = Span(e, + e2 + eg) and find W+.(c) Using the Gram Schmidt process, find an or-thogonal basis for V containing the vectorej – €2 + 2ez.

Answered: Image /qna-images/answer/4e58be4d-8cbe-496c-b57f-84b600610d92.jpg

Answered: 5. Let V = R³ and let (-, ) be the…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 41E: Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform...

See similar textbooks

Similar questions

Use the inner product u,v=2u1v1+u2v2 in R2 and Gram-Schmidt orthonormalization process to transform {(2,1),(2,10)} into an orthonormal basis.
Find a basis for R2 that includes the vector (2,2).
Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that among all the scalar multiples cv of the vector v, the projection of u onto v is the closest to u that is, show that d(u,projvu) is a minimum.
Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Define T:R2R2 by T(v)=projuv Where u is a fixed vector in R2. Show that the eigenvalues of A the standard matrix of T are 0 and 1.
7. Find an initial point P of a nonzero vector m = P& with ter-minal point O(3. 0. -5) and such that B) u is oppositely directed to v = (4, -2,-1)
Apply the Gram-Schmidt process to transform the basis vectors V1= (1,1,1), V2 = (0,1,1), V3 = (0,0,1) into an orthogonal basis (u1,u2,u3) and then normalize the orthogonal basis vectors to obtain an orthonormal basis (w1,w2,w3)
Prove that if {y1,...,yn} is an orthogonal set of nonzero vectors, then the vectors {x1,...,xn} derived from the Gram-Schmidt process satisfy xi=yi for i=1,..,n.
write the equation of the plane with normal vector n passing through the given point in the scalar form ax + by + cz = d. n = (−1, 2, 1), (4, 1, 5)
Find a basis for the set of vectors in ℝ2 on the line y = 5x.

Recommended textbooks for you

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:

9781305071742

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

5. Let V = R³ and let (-, ) be the standard dot prod- uct. (a) Calculate (3e, + 2e, – €3, 2e2 + 4e3). - (b) Let W = Span(e, + e2 + eg) and find W+. (c) Using the Gram Schmidt process, find an or- thogonal basis for V containing the vector ej – €2 + 2ez.