Purchase Solution

Linear transformations

Not what you're looking for?

Ask Custom Question

Please help me solve the following linear algebra questions involving linear transformation and matrices. (see attached)

? Let and let . Define a map by sending a vector to .

a) let and be the standard basis vectors of V. let , and be the standard basis vectors of W. Find the matrix of T with respect to these bases of V and of W.
b) let and . Prove that form a basis of V and find the matrix of T with respect to the bases of V and of W.
c) let . Show that form a basis of W. Find the matrix of T with respect to the bases of V and of W.

? Let and let be the linear transformation given by

find the matrix A of T with respect to the standard basis

of both V and W.

Purchase this Solution

Solution Summary

There are a variety of linear transformation problems here, such as "find the matrix A of T with respect to the standard basis" as well as proofs that a given vectors is a basis

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.

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.

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

Solving quadratic inequalities

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