Explore BrainMass

Explore BrainMass

    Transformation : Null Space, Range and Eigenvalues

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached problem relating to null space, range, eigenvalues and transformation.

    © BrainMass Inc. brainmass.com December 24, 2021, 5:08 pm ad1c9bdddf


    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    1) For the matrix A3, the null space denoted usually by "ker(A3)" from word "kernel", is defined as the set of solutions of equation:

    where (0) is the null vector, that is the vector (0, 0, 0) (unlike number 0, which is a simple scalar)
    Trying to solve the above equation, we get the algebraic system:

    It can be easily observed that the system is not a Cramer one, because the rank of main matrix is 1, the same as the extended matrix. That means the system is consistent, but an infinite number of solutions will be ...

    Solution Summary

    A problem relating to null space, range, eigenvalues and transformation is solved. The solution is detailed and well explained.