Purchase Solution

Properties of Elementary Matrices

Not what you're looking for?

Ask Custom Question

Please prove the statements shown below:

1. If the elementary matrix E results from performing a certain row operation on an identity matrix Im and if A is an m x n matrix, then the product EA is the matrix that results when this same roe operation is performed on A.

2. Every elementary matrix is invertible, and the inverse is also an elementary matrix.

Purchase this Solution

Solution Summary

This solution provides proof that for an elementary matrix, E, and arbitrary matrix,A; EA results in a matrix that is the same as if the row operation that created E was performed on A. Additionally, it provides proof that every E is invertible and the inverse of E is also an elementary matrix. The solution also includes a link to a source for further explanation of the concept.

Solution Preview

For 2.

Invertible means that A is square and A^-1 exists or A is nonsingular.
A is nonsingular if it's determinant is nonzero.
So you need only show that every elementary matrix is square and has a nonzero determinant.

Use the fact that det(I) = 1. and that performing row ...

Purchase this Solution

Free BrainMass Quizzes
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.

Probability Quiz

Some questions on probability

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.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts