2. Given a square matrix A, eigenvalues of A are denoted as A, and are found...

 

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2. Given a square matrix A, eigenvalues of A are denoted as A, and are found by solving det(A-AI) = 0. (a) Define matrix A to be 1 -1 0 A = -1 2 -1 0 -1 1 Find a cubic equation for the eigenvalues of this matrix. (b) Plot the cubic equation using plotting software such as Desmos, and determine the eigenvalues. (c) Every eigenvalue has an infinite set of eigenvectors v, which satisfy Av = Av, or = 6190-0) V3 V3 Choose the eigenvalue A = 3, and use this equation to generate a linear system for the components of v. Solve this linear system to obtain the eigenvector family for X = 3. 2. Given a square matrix A, eigenvalues of A are denoted as A, and are found by solving det(A-AI) = 0. (a) Define matrix A to be 1 -1 0 A = -1 2 -1 0 -1 1 Find a cubic equation for the eigenvalues of this matrix. (b) Plot the cubic equation using plotting software such as Desmos, and determine the eigenvalues. (c) Every eigenvalue has an infinite set of eigenvectors v, which satisfy Av = Av, or = 6190-0) V3 V3 Choose the eigenvalue A = 3, and use this equation to generate a linear system for the components of v. Solve this linear system to obtain the eigenvector family for X = 3.