# MATHLAB 4 - 0.6930 0.0000i 0.6930 0.0000i 0.8717 0.0000i...

• Homework Help
• 6

This preview shows page 1 - 6 out of 6 pages.

4.1>> B=[1.2 2.5;4 0.7]B =1.2000 2.50004.0000 0.7000>> [eigvec, eigval]=eig(B)eigvec =0.6501 -0.58990.7599 0.8075eigval =4.1221 00 -2.22214.2A=[1 3;-1 -8]A =1 3-1 -8>> [eigvec, eigval]=eig(A)eigvec =0.9934 -0.3276-0.1148 0.9448eigval =0.6533 00 -7.6533
x ' = x + 3 y y ' = - x - 8 y-2-101234-4-3-2-1012xyPlot is embedded to the right. This is the sae as we thought about how drift toward andhow positive or negative values of C1 and C2 affect it. 4.3>> A=[2.7 -1;4.2 3.5]A =2.7000 -1.00004.2000 3.5000>> [eigvec, eigval]=eig(A)eigvec =-0.0856 + 0.4301i -0.0856 - 0.4301i0.8987 + 0.0000i 0.8987 + 0.0000ieigval =3.1000 + 2.0100i 0.0000 + 0.0000i0.0000 + 0.0000i 3.1000 - 2.0100i
x ' = 2.7 x - y y ' = 4.2 x + 3.5 y-2-101234-4-3-2-1012xyThe imaginary part does not affect whether the solutions tend to infinity. If the realvalue is positive, then the solutions tend toward infinite. If it is negative, then it tendstoward zero.4.4>> A = [1.25, -.97, 4.6; -2.6, -5.2, -.31; 1.18, -10.3, 1.12]A =1.2500 -0.9700 4.6000-2.6000 -5.2000 -0.31001.1800 -10.3000 1.1200>> [eigvec, eigval]=eig(A)eigvec =0.7351 + 0.0000i -0.4490 - 0.2591i -0.4490 + 0.2591i-0.1961 + 0.0000i 0.3375 - 0.2242i 0.3375 + 0.2242i0.6490 + 0.0000i 0.7530 + 0.0000i 0.7530 + 0.0000ieigval =5.5698 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i -4.1999 + 2.6606i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i -4.1999 - 2.6606iUnstableThe reason is eigenvalues of the system includes real, nonzero values: the solutions arenot bounded.4.5A=[-.0558 -.9968 .0802 .0415;.598 -.115 -.0318 0;-3.05 .388 -.4650 0;0 .0805 1 0]A =-0.0558 -0.9968 0.0802 0.04150.5980 -0.1150 -0.0318 0-3.0500 0.3880 -0.4650 00 0.0805 1.0000 0>> [eigvec, eigval]=eig(A)eigvec =0.1994 - 0.1063i 0.1994 + 0.1063i -0.0172 + 0.0000i 0.0067 + 0.0000i-0.0780 - 0.1333i -0.0780 + 0.1333i -0.0118 + 0.0000i 0.0404 + 0.0000i-0.0165 + 0.6668i -0.0165 - 0.6668i -0.4895 + 0.0000i -0.0105 + 0.0000i