Purchase Solution

Subspace

Not what you're looking for?

Ask Custom Question

Linear Equation Questions. See attached file for full problem description.

Let S be the subspace....
Explain why this linear equation represents a subspace and find a basis for it.
Clearly explain why this subspace is a plane.
Find two orthogonal vectors in the plane.
Make the set you found orthonormal.
Explain why your set is a basis for the plane.
Show that the vector...is not in the plane.
Find the vector in the plane that is the closest to v.

Attachments
Purchase this Solution
Solution Summary

This is a set of questions regarding a subspace, vectors, and basis.

Solution Preview

Please see the attached file.

Proof:
(a) Since is the subspace defined by the equation , then is the set of all points that satisfy the equation. We can give a general solution. Let , then we can find two linearly independent solution and . Especially, let , we obtain the basis of . The basis is , ...

Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers

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

Probability Quiz

Some questions on probability

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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

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

View More Free Quizzes
Related BrainMass Solutions

  • Vector Space and Subspace

    ii) is a subspace of Note: i) V is a subspace of V itself. ii) The space containing only the vector is a subspace of V. It is called the zero subspace of V.

  • Matrix subspace

    204106 Matrix subspace theory Please see the attached file thank-you for your help. Let A be an n x n matrix, and suppose "T" is a subspace of .

  • Vector Subspaces

    If U is a subspace of V then V-U = also is a subspace. (Proof or counterexample) False.

  • Linear Subspace Dimension

    50416 Linear Subspace Dimension Please provide solutions to these two questions (attached). Please show how the subspace satisfies both addition & scalar multiplication!

  • Hahn Banach Theorem Application

    A subspace M of is said to be complemented in if there exists a subspace N of such that =M N, that is if , then there exists in M and in N such that , and M N . Prove that each finite dimensional subspace of is complemented in .

  • Prove that U is a Subspace of V and is Contained in W

    Then W is a subspace of V.

  • Geometric Interpretation of the Subspace

    16061 Geometric Interpretation of the Subspace Show that the set of all elements of R^2 of the form (a, -a), where a is any real number, is a subspace of R^2. Give a geometric interpretation of the subspace.

  • Properties of vector spaces.

    This set is not a subspace NOT a subspace, since: But if we multiply it by a real number: And: Thus: and this operation contradicts the subspace definition Is a subspace since: Vector subspaces must adhere to strict

  • Linear Algebra : Subspace

    Therefore, is a subspace of . Done. The subspace is varied in an attached Word document showing all calculations.

  • Vector Subspace Example

    The Solution to this equation has four free parameters, which means, that the dimension of the subspace is four. Solution calculates a dimension of subspace of vector space of polynomials. Attached as a Word document.

View More Related Solutions