ODE question I'm stuck, said use putzer algorithm to find fundemental matrix because be easier invert later for solution. Please Help, I have started it. Little shaky finding r_2 and on [2e3t I-2and e(t) = . Find the general solution to y' = Ay + e-2a) Find Fundamental Matrix– 1-2 – al1det(A – 21) = det-1=(-2- 1)(-2 – 1) – 1 = 2² + 42 + 3 = (1 + 1)(1 + 3)111 = -3, 12= -1b) Use Putzer Algorithm to find etAPo = 1;P1 = (A – 1,1)P, = (A – -31)P, =ri = e-3tr2

Answered: [-2 1) Let A = and e(t) = [3) Find the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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ODE question I'm stuck, said use putzer algorithm to find fundemental matrix because be easier invert later for solution. Please Help, I have started it. Little shaky finding r_2 and on

[2e
3t I
-2
and e(t) = . Find the general solution to y' = Ay + e
-2
a) Find Fundamental Matrix
– 1
-2 – al
1
det(A – 21) = det-
1=(-2- 1)(-2 – 1) – 1 = 2² + 42 + 3 = (1 + 1)(1 + 3)
1
11 = -3, 12
= -1
b) Use Putzer Algorithm to find etA
Po = 1;
P1 = (A – 1,1)P, = (A – -31)P, =
ri = e-3t
r2

Expert Solution

Step 1

Given matrix is $A = [\begin{matrix} - 2 & 1 \\ 1 & - 2 \end{matrix}]$

Since the matrix A is symmetric matrix, therefore corresponding eigenvalues are

$\begin{array}{rcl} λ_{1} & = & - 2 - 1 \\ = & - 3 \\ λ_{2} & = & - 2 + 1 \\ = & - 1 \end{array}$

Now,

$\begin{array}{rcl} P_{0} & = & I \\ P_{1} & = & (A - λ_{1} I) \\ = & [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}] \end{array}$

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