Write the system of equations in the image in matrix form x'_1(t)=3x_1(t)-2x_2(t)+e^tx_3(t) x'_2(t)=sin(t)x_1(t)+cos(t)x_3(t) x'_3(t)=t^2x_1(t)+tx^2(t)+x_3(t)

Burhan Hopper 2020-11-17 Answered
Write the system of equations in the image in matrix form
x1(t)=3x1(t)2x2(t)+etx3(t)
x2(t)=sin(t)x1(t)+cos(t)x3(t)
x3(t)=t2x1(t)+tx2(t)+x3(t)
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Expert Answer

Ayesha Gomez
Answered 2020-11-18 Author has 104 answers

Step 1
Now , we need to write this system of equations in matrix form .
The given system of equations is ,
x1(t)=3x1(t)2x2(t)+etx3(t)
x2(t)=sin(t)x1(t)+cos(t)x3(t)
x3(t)=t2x1(t)+tx2(t)+x3(t)
This system of equations is in 3 variables , x1(t),x2(t),x3(t)
Therefore , the matrix formed will be a 3×3 matrix .
Step 2
We can write down the system of equations in the form X(t)=AX(t).
Hence , we get,
[x1(t)x2(t)x3(t)]=[32etsin(t)0cos(t)t2t1][x1(t)x2(t)x3(t)]
Results: The system of equations can be written in matrix form as, [x1(t)x2(t)x3(t)]=[32etsin(t)0cos(t)t2t1][x1(t)x2(t)x3(t)]

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Jeffrey Jordon
Answered 2021-11-03 Author has 2070 answers

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