# SECTION 9.3# Example 1with(linalg);

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AI := matrix([[1,2,1,1,0,0],[1,3,2,0,1,0],[1,0,1,0,0,1]]);

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?addrowaddrow(AI,1,2,-1): addrow(%,1,3,-1); #Add -1 times row 1 to rows 2 and 3

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addrow(%,2,3,2); # Add 2 times row 2 to row 3

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addrow(%,2,1,-2); # Add -2 times row 2 to row 1;

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mulrow(%,3,1/2);# Multiply row 3 by 1/2

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addrow(%,3,1,1): addrow(%,3,2,-1); #Add row 3 to row 1, and -1 times row 3 to row 2

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#Example 2A := [[t^2+1,cos(t)],[exp(t),1]];

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evalm(A); # Display as a 2 by 2 matrix

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# (a)diff(A,t);

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evalm(%);

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# (b)B := matrix(2,2);

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Int(A[1,1],t=0..1); B[1,1] := value(%);

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Int(A[1,2],t=0..1); B[1,2] := value(%);

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Int(A[2,1],t=0..1); B[2,1] := value(%);

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Int(A[2,2],t=0..1); B[2,2] := value(%);

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evalm(B);

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# Example 3x := [cos(omega*t),sin(omega*t)];

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A := matrix(2,2,[[0,-omega],[omega,0]]);

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diff(x,t);

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evalm(A &* x);

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# Therefore dx/dt = AX