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Hi, I need help with parts (i), (ii) and (iii). 7. Determine the real canonical form y = By, B = G'lAG 0f the dynamical

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Hi, I need help with parts (i), (ii) and (iii).

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7. Determine the real canonical form y = By, B = G'lAG 0f the dynamical system 5: = Ax for the following matrices A. Determine the stability and type of the equilibrium point Xe = 0. Find the general solution y and draw the phase portrait on the (y1,y2)plane. Use the transformation X=Gy to sketch the phase portrait on the (11:1, x2)plane. You are encouraged to use Maple/Matlab/Mathematica to verify your sketches. (1)A:[_12 E3] (ii)A=[: 2] (111) A=[:i i] 7. l (i) Stable node. Eigenvalues are E (5 j: V13). 5(1+\\/E>%(1x/E)] G: 1 1 1 0 (ii) Unstable bicritical node (\"star\"). Eigenvalue is 4. G = [ 0 1 ] (iii) (Stable) centre. Eigenvalues are ii. G = [ 1 _01 J

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