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midIchosen

# midIchosen - Potential problems for midterm I 7.2.26 Verify...

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Potential problems for midterm I 7.2.26 Verify that Φ( t ) = e t - e 2 t e 3 t 2 e t 2 e 2 t - e 3 t - 2 e t e 2 t - 2 e 3 t is a solution to the differential equation Φ 0 ( t ) = - 1 - 2 / 3 - 5 / 3 0 5 / 3 2 / 3 6 4 / 3 16 / 3 Φ( t ) This is done by plugging stuff in: Φ 0 ( t ) = e t - 2 e 2 t 3 e 3 t 2 e t 4 e 2 t - 3 e 3 t - 2 e t 2 e 2 t - 6 e 3 t and - 1 - 2 / 3 - 5 / 3 0 5 / 3 2 / 3 6 4 / 3 16 / 3 e t - e 2 t e 3 t 2 e t 2 e 2 t - e 3 t - 2 e t e 2 t - 2 e 3 t = - e t - 4 / 3 e t + 10 / 3 e t e 2 t - 4 / 3 e 2 t - 5 / 3 e 2 t - e 3 t + 2 / 3 e 3 t + 10 / 3 e 3 t 0 + 10 / 3 e t - 4 / 3 e t 0 + 10 / 3 e 2 t + 2 / 3 e 2 t 0 - 5 / 3 e 3 t - 4 / 3 e 3 t 6 e t + 8 / 3 e t - 32 / 3 e t - 6 e 2 t + 8 / 3 e 2 t + 16 / 3 e 2 t 6 e 3 t - 4 / 3 e 3 t - 32 / 3 e 3 t = e t - 2 e 2 t 3 e 3 t 2 e t 4 e 2 t - 3 e 3 t - 2 e t 2 e 2 t - 6 e 3 t 7.3.7 Determine if the vectors x = (1 , 2 , 1), y = (0 , 0 , 1) and z = (1 , 0 , 1) are linearly dependent or indepen- dent. If they are dependent, find a linear relation among them. We look at the determinant of the matrix made up of these vectors (as columns). det 1 0 1 2 0 0 1 1 1 = 1 · det 0 0 1 1 !

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midIchosen - Potential problems for midterm I 7.2.26 Verify...

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