Consider the linear system X' = AX, where A is a 2 x 2 matrix with eigenvectors %3D and corresponding to the eigenvalues ŋ = -1 and r2 = 2, respectively. Find the funda- mental matrix of the system such that D(0) = I.

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Q: 6. Solve the following Cauchy-Euler equation. (Section 4.7) x?y" + 5xy' + 4y = 0

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Q: 1+t t -t ₁ -²₁ ) = e²₁ et4 1 1-t

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Q: write the Matrix exponential For to show why ett - fet o #* = [6* > ] O A = [1 2] 3

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Q: Please no written by hand solutions Solve the system of differential equations x₁'= -464x₁ + 1683x2…

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A: Simply solve the given differential equation and compare with the  given solution.

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.