# Let each matrix in Exercises 1–6 act on C2. Find the

## Problem 1E Chapter 5.5

Linear Algebra and Its Applications | 5th Edition

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Linear Algebra and Its Applications | 5th Edition

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Problem 1E

Let each matrix in Exercises 1–6 act on C2. Find the eigenvalues and a basis for each eigenspace in C2.

Step-by-Step Solution:

Solution 1EStep 1 Consider the matrix .The objective is to find the eigenvalues and a basis for each eigenspace in The characteristic equation of A is, Use the quadratic formula to find the eigenvalues: Therefore the eigenvalues are Step 2 Find the eigenvector corresponding to the eigenvalue Then, The above two equations determine the same relationship between The second equation leads to, .

Step 3 of 3

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