Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. -1 -1] A =1 2 1 -1 Using this diagonalization, write three matrices product in its simplest form for A10. Is it same for any power Akfor this special matrix A.
Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. -1 -1] A =1 2 1 -1 Using this diagonalization, write three matrices product in its simplest form for A10. Is it same for any power Akfor this special matrix A.
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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![Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1,
1.
-1 -1]
A= 1
2
1
-1
Using this diagonalization, write three matrices product in its simplest form for Al0. Is it
same for any power Akfor this special matrix A.
Part: c:
Suppose the rabbit-wolf population (rw) are governed by the following coupled differential
equation
dr
= ar + bw
dt
dw
= cr + dw
dt
Where a, b, c and d are some unknown constants.
If this coupled differential equation is written as a vector differential equation as
du
= Au
dt
[a b]
where A="
lc dl
1 = |" and u=
And given that eigenvalues of A are -3 and -1 with corresponding eigenvectors vi=
E&v= find the rabbit and wolf population i.e the functions r(t) and w(t) at any time t
if initial rabbit population ro is 2 and wolf population wo is 3?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd695a545-e62b-4c0e-9f8a-94327fa9e59d%2Fb9a95398-90a0-4005-bb5b-c0831336f7f3%2Fozp4nc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1,
1.
-1 -1]
A= 1
2
1
-1
Using this diagonalization, write three matrices product in its simplest form for Al0. Is it
same for any power Akfor this special matrix A.
Part: c:
Suppose the rabbit-wolf population (rw) are governed by the following coupled differential
equation
dr
= ar + bw
dt
dw
= cr + dw
dt
Where a, b, c and d are some unknown constants.
If this coupled differential equation is written as a vector differential equation as
du
= Au
dt
[a b]
where A="
lc dl
1 = |" and u=
And given that eigenvalues of A are -3 and -1 with corresponding eigenvectors vi=
E&v= find the rabbit and wolf population i.e the functions r(t) and w(t) at any time t
if initial rabbit population ro is 2 and wolf population wo is 3?
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