Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 51E
Related questions
Question
Expert Solution
Step 1
Given:
To Determine:
A is defective or not.
Defective matrix:
A defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors.
Step 2
Here,
First, the find eigenvalues and eigenvectors
Start from forming a new matrix by subtracting λ from the diagonal entries of the given matrix:
Find the determinant of the obtained matrix:
Thus, the root are
These are the eigen values.
Step by step
Solved in 3 steps
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