Purchase Solution

Linear algebra

Not what you're looking for?

Ask Custom Question

Show that the set of all elements of R^3 of the form (a + b, -a, 2b), where a and b are any real numbers, is a subspace of R^3. Show that the geometric interpretation of this subspace is a plane and find its equation.

Purchase this Solution

Solution Summary

The geometric interpretation of subspaces on planes are found. The expert finds an equation of subspaces using real numbers.

Solution Preview

The set V = {(a+b, -a, 2b): a, b are real numbers} is closed with respect to addition and multiplication by scalar since:
(1) (a+b, -a, 2b) + (c+d, -c, 2d) = (a+c+b+d, -(a+c), 2(b+d))
and ...

Purchase this Solution


Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Graphs and Functions

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

Solving quadratic inequalities

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

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

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.