# Certai isomorphic modules

Not what you're looking for?

Need stepwise solution of the attached problem.

##### Purchase this Solution

##### Solution Summary

It is proved that the K-module of polynomials of degree less than n is isomorphic to the module K^n.

##### Solution Preview

Dear student,

See the attached file.

Let us denote the K-module of all polynomials in K[x] of degree less than n by K_n[x].

Let us construct the mapping f: K_n[x] → K^n as follows: f(a_0+a_1 x+⋯+a_(n-1) x^(n-1))=(a_0,a_1,...,a_(n-1)), for any polynomial 〖(a〗_0+a_1 x+⋯+a_(n-1) x^(n-1)).

It is obvious that f is injective. Indeed, if 〖 polynomials (a〗_0+a_1 x+⋯+a_(n-1) ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### 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

##### 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.

##### 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.