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

(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

Observe the general te...

1 4
A =
2 3
-2+2(52)
2+5
9 16
A2
1
8 17
3-1+5
1+2(5)
2+52+2(5
3 -1+51+2(5)
41 84
A3
1
42 83
-2+2(5"
1+2(5")
2+5"
1
A'"
3-1+5"
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1 4 A = 2 3 -2+2(52) 2+5 9 16 A2 1 8 17 3-1+5 1+2(5) 2+52+2(5 3 -1+51+2(5) 41 84 A3 1 42 83 -2+2(5" 1+2(5") 2+5" 1 A'" 3-1+5"

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