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Asked Dec 1, 2019
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Linear algebra. Please answer part (b)

(4 Let A be the 2 x 2 matrix given below
1 4
A =
2
3
(a) Show that A is diagonalizable and find a matrix P such that P-1AP is diagonal.
(b) Find an expression for A" for any integer n > 0.
(c) Compute eA, the matrix exponential of A.
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(4 Let A be the 2 x 2 matrix given below 1 4 A = 2 3 (a) Show that A is diagonalizable and find a matrix P such that P-1AP is diagonal. (b) Find an expression for A" for any integer n > 0. (c) Compute eA, the matrix exponential of A.

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Expert Answer

Step 1
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1 4 The given matrix is, A| 2 3 A is diagonalizable, for a matrix P such that, P-1AP = D 1 and a For the matrix A, the eigen values are -1 and 5 and the eigen vectors are a respectively for any non-zero scalar a (2 -1 1 Thus, P = 1 and P Then, 1 -1 2 1

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2 -1)1 4 1 1 2 3-1 2 1 -1 0 D = 0 5 Here, A is diagonalizable. This implies PP AP PD LAPP = PDP A PDP A(PDP) APDP(PDP A PD" P (PDF") (PDF ).. up to n times

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