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Linear Algebra With Applications
Found in: Page 345
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

For a given eigenvalue, find a basis of the associated eigenspace. Use the geometric multiplicities of the eigenvalues to determine whether a matrix is diagonalizable. For each of the matrices A in Exercises 1 through 20, find all (real) eigenvalues. Then find a basis of each eigenspace, and diagonalize A, if you can. Do not use technology


The given matrix A is not diagonalizable.

See the step by step solution

Step by Step Solution

Step 1: Algebraic Versus.

Algebraic versus geometric multiplicity If λ is an eigenvalues of a square matrix A,





Step 2: Solve the values

For λ=0


The basic of the eigenspace is 010=v1

Step 3: Find the value.

For λ=1 , we get


The basic of this eigenspace is 1-12=v2

Therefore, the gemu1<almu1. So A is not diagonalizable.

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