Question

what is the general pattern of the solution of any linear system.

a)answer with a set

b)answer with words

Answer #1

Is the solution set of a non-homogeneous linear system "Ax=b" a
subspace?
Give reason(s) to support your answer

Consider the linear system
dY/dt=(0 2 −2 −1)Y
(a) Find the general solution.
(b) Find the particular solution with the initial value
Y0=(−1,1).

Use the elimination method to find a general solution for the
linear system: x'=3x-4y y'=4x-7y

Find general solution to the linear system of first-order
differential equation. Explain and show all steps
X' = [ 6 -1 ] X
[ 5 4 ]

Find the general solution to the following linear system around
the equilibrium point:
x '1 = 2x1 + x2
x '2 = −x1 + x2
(b) If the initial conditions are x1(0) = 1 and x2(0) = 1, find
the exact solutions for x1 and x2.
(c) Plot the exact vector field (precise amplitude of the
vector) for at least 4 points around the equilibrium, including the
initial condition.
(d) Plot the solution curve starting from the initial condition
x1(0)...

1. Find the general solution of the first order linear
differential equation: 2*x*dy/dx -y-3/sqrt(x)=0. sqrt() = square
root of ().
2. Are there any transient terms in the general solution?
Justify your answer.

Find the general solution of the homogeneous system below. Give
your answer as a vector.
x1 + 2x2 - 3x3 = 0
4x1 + 7x2 - 9x3 = 0
-x1 - 4x2 + 9x3= 0

What is the general solution to this system of diff. eq.?
x1' = x1 + 2x2 +
2x3
x2' = 2x1 + 7x2
+x3
x3' = 2x1 + x2 +
7x3

LAB 3.1 Bifurcations in Linear Systems
In Chapter 3, we have studied techniques for solving linear
systems. Given the coefﬁcient matrix for the system, we can use
these techniquesto classify the system, describe the qualitative
behavior of solutions, and give a formula for the general solution.
In this lab we consider a two-parameter family of linear systems.
The goal is to better understand how different linear systems are
related to each other, or in other words, what bifurcations occur
in...

1.Consider the following linear system in augmented matrix
form
[2 4−3 | 11
1 2−1 | 4]
(a) Find the general solution of the linear system.
(b) Find two particular solutions to this linear system.

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