Math Problem Statement

Matrix A is given as: A = [ [3, 0, 2, 0], [1, 3, 1, 0], [0, 1, 1, 0], [0, 0, 0, 4] ]. Find a basis for the eigenspace corresponding to the eigenvalue λ = 4. Explain your answer and show your work.

Solution

Problem Statement

The matrix AA is given as:

3 & 0 & 2 & 0 \\ 1 & 3 & 1 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 4 \end{bmatrix}$$ We are tasked to find a basis for the eigenspace corresponding to the eigenvalue $$\lambda = 4$$. ### Solution The eigenspace is the set of all eigenvectors corresponding to a given eigenvalue, together with the zero vector. To find the

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Eigenvalues and Eigenvectors
Eigenspaces

Formulas

(A - λI)v = 0
Eigenspace basis vectors

Theorems

Eigenvalue equation
Linear independence of eigenvectors

Suitable Grade Level

Undergraduate Mathematics

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