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Consider the linear system x' = < b m a t r i x > x. Find the eigenvalues and eigenvectors for the coefficient matrix. λ1 = v⃗1 = and λ2 = v⃗2 = For each eigenpair in the previous part, form a solution of x' = Ax. Use t as the independent variable in your answers. x⃗1(t) = x⃗2(t) =
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SOLVED:Find the eigenvalues and a basis for each eigenspace of the linear operator defined by the stated formula. [Suggestion: Work with the standard matrix for the operator.] T(x, y)=(x 4 y, 2 x 3 y)
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