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# Matrices

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Let B = . Find each of the following. You may use a calculator to replace hand calculation for row reduction and finding the characteristic polynomial. Show your work; don't just write down the answers.

(a) Find the characteristic polynomial of "A".
(b) Find the eigenvalues of "A"; for each, find the algebraic multiplicity.
(c) Find a basis for each eigenspace.
(d) Diagonalize "A" ; that is, find: S , &#923; , and, S-1 such that A = S &#923; S-1 .

https://brainmass.com/math/linear-algebra/matrix-theory-functions-204092

#### Solution Preview

Dear Student
The detailed step by step solution is given in the attached solution file.

Let B = . Find each of the following. You may use a calculator to replace hand calculation for row reduction and finding the characteristic polynomial. Show your work; don't just write down the answers.

(a) Find the characteristic polynomial of "A".
(b) Find the eigenvalues of "A"; for each, find the algebraic multicplicity.
(c) Find a basis for each eigenspace.
(d) Diagonalize "A" ; that is, find: S , Λ , and, S-1 such that A = S Λ S-1 .
Solution:
A is a block triangular with diagonal blocks  ...

#### Solution Summary

This provides an example of finding characteristic polynomial, eigenvalues, algebraic multiplicity, eigenspace.

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