Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1,1.-1 -1]A= 121-1Using this diagonalization, write three matrices product in its simplest form for Al0. Is itsame for any power Akfor this special matrix A.Part: c:Suppose the rabbit-wolf population (rw) are governed by the following coupled differentialequationdr= ar + bwdtdw= cr + dwdtWhere a, b, c and d are some unknown constants.If this coupled differential equation is written as a vector differential equation asdu= Audt[a b]where A="lc dl1 = |" 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 tif initial rabbit population ro is 2 and wolf population wo is 3?

The matrix A is diagonalizable if there exist an invertible matrix P such that P-1AP is a diagonal…

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.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.4: Orthogonal Diagonalization Of Symmetric Matrices

Problem 27EQ

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Question

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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