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Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 13E
Related questions
Question
Find an orthogonal or unitary diagonalizing matrix for each of the following:
Expert Solution
Step 1
Suppose, the matrix is:
.
Firstly, solve the characteristic equation and find the eigenvalues.
So, the eigenvalues are:
.
Step 2
Now, find the eigenvectors.
For, ,
Apply,
So, the equations are:
Suppose, .
So,
So, the eigenvector is:
.
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