Linear algebra questions
Not what you're looking for?
32. Answer the following:
a. Let (where is the vector space of 2 by 2 matrices.) Find an example that shows U is NOT a subspace of .
The matrix where U=[1 0; 0 1] the det=1. This would not be a subspace of M22.
b. Let where is the vector space of real-valued functions defined on the interval [0, 2]. Show that is a subspace of this vector space.
1. V contains the 0 vector since
2. V is closed under scalar multiplication since u = [0,2] then cu = [0,2c]
3. V is closed under addition since ?
Purchase this Solution
Solution Summary
Linear algebra questions are demonstrated in this solution.
Solution Preview
For question (a) you need to show that the set U of matrices with determinant 0 is not a subspace of M_22. It's not enough to show that there is a matrix, that is not in U. There are matrices in U, there are matrices outside of U. What you need to show is that there are two matrices in U whose linear combination is not in U (or, at least the sum of them is not in U). ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
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.