This document contains the solutions to multiple problems involving matrices and systems of equations. It provides the steps and results for: 1) Finding the characteristic polynomials, eigenvalues, and eigenvectors of two matrices A and B. 2) Calculating the transition matrices for systems described by A and B. 3) Describing two cases for transforming between the time and frequency domains.

1. CONTROL II……………….PRUEBAN.-2…2DOPARCIAL……..
GRUPON.-1
1.-)
A = 1 3 0
4 2 2
0 -2 1
coef= 1.0000 -4.0000 -3.0000 6.0000
polcaracA =x^3 - 4*x^2 - 3*x + 6
raicesA = 4.3723
-1.3723
1.0000
B = 1 -2 6
2 -3 4
3 -2 0
coef= 1.0000 2.0000 -9.0000 -14.0000
polcaracB =x^3 + 2*x^2 - 9*x - 14
raicesB = 2.8595
-3.4337
-1.4259
2.-)usode eig
A valpropA = 4.3723
-1.3723
1.0000
mattran =

2. [ (3*exp((3*t)/2)*(cosh((33^(1/2)*t)/2) - (33^(1/2)*sinh((33^(1/2)*t)/2))/33))/2- exp(t)/2,
(2*33^(1/2)*exp((3*t)/2)*sinh((33^(1/2)*t)/2))/11,(3*exp((3*t)/2)*(cosh((33^(1/2)*t)/2) -
(33^(1/2)*sinh((33^(1/2)*t)/2))/33))/4- (3*exp(t))/4]
[ (8*33^(1/2)*exp((3*t)/2)*sinh((33^(1/2)*t)/2))/33,
exp((3*t)/2)*(cosh((33^(1/2)*t)/2) +(33^(1/2)*sinh((33^(1/2)*t)/2))/33),
(4*33^(1/2)*exp((3*t)/2)*sinh((33^(1/2)*t)/2))/33]
[ exp(t) - exp((3*t)/2)*(cosh((33^(1/2)*t)/2) - (33^(1/2)*sinh((33^(1/2)*t)/2))/33),
-(4*33^(1/2)*exp((3*t)/2)*sinh((33^(1/2)*t)/2))/33, (3*exp(t))/2 -
(exp((3*t)/2)*(cosh((33^(1/2)*t)/2) - (33^(1/2)*sinh((33^(1/2)*t)/2))/33))/2]
B valpropB= 2.8595
-3.4337
-1.4259
mattran =
[ - 8*symsum(-exp(r3*t)/(3*r3^2+ 4*r3 - 9), r3 inRootOf(s3^3 + 2*s3^2 - 9*s3 - 14, s3)) -
3*symsum(-(r3*exp(r3*t))/(3*r3^2+ 4*r3 - 9), r3 inRootOf(s3^3 + 2*s3^2 - 9*s3 - 14, s3)) -
symsum(-(r3^2*exp(r3*t))/(3*r3^2+ 4*r3 - 9), r3 inRootOf(s3^3 + 2*s3^2 - 9*s3 - 14, s3)),
12*symsum(-exp(r3*t)/(3*r3^2+ 4*r3 - 9), r3 inRootOf(s3^3+ 2*s3^2 - 9*s3 - 14, s3)) +
2*symsum(-(r3*exp(r3*t))/(3*r3^2+ 4*r3 - 9), r3 inRootOf(s3^3 + 2*s3^2 - 9*s3 - 14, s3)),
- 10*symsum(-exp(r3*t)/(3*r3^2 + 4*r3 - 9), r3 inRootOf(s3^3+ 2*s3^2 - 9*s3 - 14, s3)) -
6*symsum(-(r3*exp(r3*t))/(3*r3^2+ 4*r3 - 9), r3 inRootOf(s3^3 + 2*s3^2 - 9*s3 - 14, s3))]
………………………………………………….
3.-)…………………………
AVectorespropios
-0.6077 -0.6951 -0.4472
-0.6831 0.5497 -0.0000
0.4051 0.4634 0.8944
Valorespropios
4.3723 0 0
0 -1.3723 0
0 0 1.0000

3. B Vectorespropios
-0.6077 -0.6951 -0.4472
-0.6831 0.5497 -0.0000
0.4051 0.4634 0.8944
Valorespropios
4.3723 0 0
0 -1.3723 0
0 0 1.0000
4.-)…………usode en vezde AC=[ -a, c][ d, -b]
inversa=[ (b+ s)/(a*b - c*d + a*s + b*s + s^2), c/(a*b - c*d + a*s + b*s + s^2)]
[ d/(a*b- c*d + a*s + b*s + s^2), (a+ s)/(a*b - c*d + a*s + b*s + s^2)]
determinante =
a*b - c*d + a*s + b*s + s
5.-)……………………..doscasos de FTee y de ee FT
Caso a.-->k =1
G = 2
-------------------------
21 s^3 + 13 s^2 + 5 s + 1
-0.6190 -0.2381 -0.0476
1.0000 0 0
0 1.0000 0
1
0
0
Caos b matrices A, B , C , D

4. GRUPON.-2…………………………
1.-)POLINOMIOSDE A Y B NUMERICOS NOLITERALES
raizA =
3.5616
1.0000
-0.5616
raizB = -3.7347 + 0.0000i
1.3673 + 1.1591i
1.3673 - 1.1591i
2.-)USODEL eigymatrizde transicion
valorA = 3.5616
-0.5616
1.0000
valorB=-3.7347 + 0.0000i
1.3673 + 1.1591i
1.3673 - 1.1591i
3.-)..
vectorespropiosde matrizA
-0.5882 0.7333 -0.5547
-0.7533 -0.5726 0
0.2941 -0.3667 0.8321
D =3.5616 0 0
0 -0.5616 0
0 0 1.0000
vectorespropiosde matrizB

5. 0.7762 + 0.0000i -0.4101 - 0.2193i -0.4101 + 0.2193i
0.3356 + 0.0000i -0.7621 + 0.0000i -0.7621 + 0.0000i
-0.5337 + 0.0000i -0.4365 - 0.1112i -0.4365 + 0.1112i
D = -3.7347 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 1.3673 + 1.1591i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 1.3673 - 1.1591i
4.-)usode A envezde C
C =[ -2*a, 2*c]
[ 2*d, -2*b]
D =[ (2*b + s)/(4*a*b - 4*c*d + 2*a*s + 2*b*s + s^2), (2*c)/(4*a*b - 4*c*d + 2*a*s + 2*b*s +
s^2)]
[ (2*d)/(4*a*b - 4*c*d + 2*a*s + 2*b*s + s^2), (2*a + s)/(4*a*b - 4*c*d + 2*a*s + 2*b*s + s^2)]
E =4*a*b - 4*c*d + 2*a*s + 2*b*s + s^2
5.-) dos casos