Query 28 Differential Equations

Question: Diagonalize the matrix [2, 3; 2, 3].

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Question: Find the algebraic and geometric multiplicity of each eigenvalue and, if possible, diagonalize the matrix

[7, -2, 2; 8, -1, 4; 8, 4, -1 ].

The characteristic equation of this matrix is (lambda - 3)^2 ( lambda + 1).

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Question: Find the algebraic and geometric multiplicity of each eigenvalue and, if possible, diagonalize the matrix

[ 5, -1, 1; 14, -3, 6; 5, -2, 5 ].

The characteristic equation of this matrix is (lambda - 2)^2 ( lambda -3).

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Question: Solve the system

y ' = [ -4, -6; 3, 5 ] y + [e^(2 t) - 2 e^t; -e^(2 t) + e^t]

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Question: Solve

x '' = [ 6, 7; -15, -16] x

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