Find the matrix of the mapping (x, y) 7 → (3x + y, x + 3y). Using any method you prefer, find alleigenvectors of the mapping and the corresponding eigenvalues.

Question

Find the matrix of the mapping (x, y) 7 → (3x + y, x + 3y). Using any method you prefer, find alleigenvectors of the mapping and the corresponding eigenvalues.
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Solution 1

Sure, let's start by finding the matrix of the mapping. The mapping is given by (x, y) 7 → (3x + y, x + 3y). This can be written in matrix form as:

[3 1]
[1 3]

Next, we find the eigenvalues. The eigenvalues of a matrix A are the roots of the characteristic equation, which is given by det(A Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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