Dimension, Linear Dependence
Not what you're looking for?
Please provide a semi-detailed response for these *two* questions (attached).
In each of the following exercises, we shall use the notation f(x) to denote the function x→f(x), x ε R. In each case, V will denote the vector space of all real-valued functions on the real line, with the vector operations defined point-wise. In each case, determine whether or not the given set is linearly independent and compute the dimension of the linear subspace spanned by the set.
18. {1, eax, ebx}, a≠b.
23. {1, cos2x, sin2x}.
Purchase this Solution
Solution Summary
This solution is comprised of a detailed explanation to determine whether or not the given set is linearly independent and compute the dimension of the linear subspace spanned by the set.
Solution Preview
Please see the attachment.
Problem #18
Suppose holds for all real number . Here . Let and we get . Without the loss the generality, assume . Now let . If , then we get . Then ...
Purchase this Solution
Free BrainMass Quizzes
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
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.
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.