Purchase Solution

Linear Algebra - Orthogonal Bases

Not what you're looking for?

Ask Custom Question

Please see the attached file for the fully formatted problems.

Let V = Span ((1, -1, 0, 2), (1, 0, 1, 1)) C R^4, and let b = (1, -3, 1, 1).

a. Find an orthogonal basis for V.
b. Use your answer to a to find p = proj_v b.
c. Letting

A = [ 1 1
-1 0
0 1
2 1]

user your answer to b to give the least squares solution of Ax - b.

Attachments
Purchase this Solution
Solution Summary

Orthogonal bases are investigated in this solution, which is given by step by step equations in an attached Word document.

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Linear Algebra: Orthogonal Bases

    175274 Linear Algebra: Orthogonal Bases Let A be an n X n matrix and, as usual, let a_1, ..., a_n denote its column vectors. a. Suppose a_1,...,a_n form an orthonormal set. Show that A^-1 = A^T. b. Suppose a_1,...

  • bases of the kernel and image of the orthogonal projection

    333300 Find bases of the kernel and image of the orthogonal projection. Please see attached file for all the questions with complete details. 1. Find bases of the kernel and image of A (or the linear transformation T(x) = Ax). 3.

  • To show a given matrix is orthogonal

    45926 To show a given matrix is orthogonal Linear Algebra Matrices (IX) Orthoganal Matrix

  • Inner product spaces

    3096 Linear Algebra -- Inner Product Spaces In C[-pi, pi] with inner product defined by (6), show that cos mx and sin nx are orthogonal and that both are unit vectors. Determine the distance between the two vectors.

  • Find a unitary matrix which is not orthogonal and an orthogonal matrix which is not unitary.

    158497 Find a Unitary Matrix Which is Not Orthogonal This is for #1 section 8.4 in Hoffman and Kunze's Linear Algebra book. Any help and detailed explanations will be greatly appreciated!

  • Inner Product Space, Linear Operators, Commutativity and Standard Inner Product

    158494 Inner Product Space, Linear Operators, Commutativity and Standard Inner Product This is for #2 & 4 section 8.3 in Hoffman and Kunze's Linear Algebra book. Any help and detailed explanations will be greatly appreciated!

  • Orthogonal projection

    175675 Linear Algebra : Orthogonality Please see attached file. Please see the attachment. This provides an example of finding an orthogonal projection.

  • Linear Algebra - Four Fundamental Subspaces & Orthogonal Complement

    175058 Linear Algebra - Four Fundamental Subspaces Please show each step of your solution. Thank you. Give a basis for the orthogonal complement of each of the following subspaces of R^4. a. V = Span ((1, 0, 3, 4), (0, 1, 2, -5)) b.

  • How do you prove V = (V^1)^1?

    Linear Algebra Let V belonging to R^n be a subspace. Show that V belongs to (V^1)^1. Do you think more is true? Please see the attachment. Proof: We know that . means that is perpendicular to . In another word, .

View More Related Solutions