Question

What is the relationship between the vector fields given as x ̇ = Ax y x ̇ = κAx Comment the relationship for κ <0 and κ> 0

Answer #1

The work should be done using MATLAB
4. Vector Fields
Show the vector fields for the following (on separate graphs)
and include these graphs in your project:
F = < -y, x>
G = < x,y>
H = < 0, x>
K = < 2x-y, 0>
L = <y,ex>

If the relationship between x and y is given by y=0.3x+0.8, what
is the correlation coefficient between x and y?

Given the following vector X, find a non-zero square matrix A
such that AX=0:
You can resize a matrix (when appropriate) by clicking and dragging
the bottom-right corner of the matrix.
x = [-1]
[10]
[-4]
This is a 3x1 matrix.

Is W = {y(x) = (ax+b)e^−x}where a,b ∈ R are arbitrary constants,
is a vector space? If yes, ﬁnd its dimension. Give explanations

Which of the following vector fields are conservative?
(i)
F(x, y) =
(7x6y6 +
3) i +
(6x7y5 +
7) j
(ii)
F(x, y) =
(6ye6x +
sin 3y) i +
(e6x +
3x cos 3y) j
(iii)
F(x, y) =
7y2e7xy i
+ (7 +
xy) e7xy j

given the equation of a line ax+by+c=0 how can i find the normal
vector to it??

Given the function f (x, y) = ax^2
2 + 2xy + ay.y
2-ax-ay. Take
for a an integer value that is either greater than 1 or less
than -1, and
then determine the critical point of this function. Then
indicate whether it is
is a local maximum, a local minimum or a saddle point.
Given the function f (x, y) = ax^2 +2 + 2xy + ay^2-2-ax-ay.
Take
for a an integer value that is either greater than 1...

For the given function u(x, y) = cos(ax) sinh(3y),(a >
0);
(a) Find the value of a such that u(x, y) is harmonic.
(b) Find the harmonic conjugate of u(x, y) as v(x, y).
(c) Find the analytic function f(z) = u(x, y) + iv(x, y) in
terms of z.
(d) Find f ′′( π 4 − i) =?

We wish to look at the relationship between y and x. Summary
measures are given below: n=5, xbar=9.4, ybar=17.2, SSxx=137.2,
SSyy=242.8, and SSxy=-169.4 Find the t test statistic for the
hypothesis H0: β1=0 vs Ha: β1≠0.

Suppose E⃗ =2A⃗ +
3B⃗ where vector A⃗ has
components Ax = 5, Ay = 2 and
vector B⃗ has components Bx =
-3, By = -5.
What is the x-component of vector E⃗ ?
What is the y-component of vector E⃗ ?
What is the magnitude of vector E⃗ ?
What is the direction of vector E⃗ ?

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