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Express system of differential equations in matrix notation

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MATH 54 QUIZ 11-

 

1. Express the given system of differential equations in matrix notation.

 

x'1 = -2x2 + x1 - 4x3

 

x'2 = 3x3 + x2 - x1

 

x'3 = -x1 + 2x3 - 3x2

 

2. Find a 4 × 4 matrix A with constant coefficients such that x(t) = 783_Figure.pngis a solution to x'(t) = Ax(t).

 

3. Show that the following collection of vector-valued functions is linearly independent on R:

 

1123_Figure1.png

 

4. Find a general solution of the system x'(t) = Ax(t), where A = 793_Figure2.png

 

5. Find the solution to the system x'(t) = 953_Figure3.pngx(t) which satisfies x(0) =2035_Figure4.png

Reference no: EM131075617

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