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Linear Algebra With Applications
Found in: Page 323
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

Find all 2×2 matrices for which e1=(10) is an eigenvector with associated eigenvalue 5.

So, the required matrix is 5b0d.

See the step by step solution

Step by Step Solution

Step 1: Define the eigenvector

Eigenvector: An eigenvector of A is a nonzero vector v in Rn such that Av=λv, for some scalar λ.

Step 2: Solve for A

If is an Eigen vector of A this means that:


Now let A=abcd,v=10, and λ=5.

We want to solve for A.

Step 3: Evaluation

To do this we will replace everything into the equation Av=λv' and we will have:

v=λvabcd10=510 ac =50 a=5 c=0

b,d are any real number

Thus, all matrices of the form 5b0dwill satisfy the given requirements.

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