Homework Statement
Consider the population model
dP/dt = -P^2/50 + 2P
for a species of fish in a lake. Suppose it is decided that fishing will be allowed, but
it is unclear how many fishing licenses should be issued. Suppose the average catch
of a fisherman with a license is 3 fish per...
Homework Statement
An affine transformation T : R^n --> R^m has the form T(x) = Ax + y, where x,y are vectors
and A is an m x n matrix and y is in R^m. Show that T is not a linear transformation when
b != 0.
Homework Equations
There are couple of useful definitions, but I think this one...
Make a truth table to see why.
X can equal only 1 or 0 thus the truth table for x*x is below :
--------
x x x*x
0 0 0
1 1 1
-------
As you see if X = 0, then X*X = 0 = X, and if X = 1, then X*X = 1 = X. Thus X*X = X
In the last row you have this : [0 0 0 0 1] which means this in equation form,
0X1 + 0X2 + 0X3 + 0X4 = 1, which means 0 = 1. This is impossible mathematically, right?
Because a 0 cannot never equal 1, which means that the system is inconsistent, or no solution. So Yes you are correct as to...
Its ok, the problem is trying to make you think hard, but I think once you thought about
the problem a little, you should then confirm it by solving the matrix.
Oh, wait see this :
The original matrix :
[3 -2 0 1 1]
[1 2 -3 1 -1]
[2 4 -6 2 0]
realize that the last row is a multiple of row2. Lets scale the last row3 so we have :
[3 -2 0 1 1]
[1 2 -3 1 -1]
[1 2 -3 1 0]
Notice something there?
>>"What I have done is replace the 2nd equation by itself + 1 times the first equation."
See thats the part thats bugging me. From middle school I have took that method as
granted. Do you think that there if a formal proof of why that method would work? Or
is it just drawn from intuitive reason...
Say there are these systems of equations :
x - 2y + z = 0
2y - 8z = 8
-4x + 5y + 9z = -9
In matrix form, it can be represented like this :
--
[1 -2 1 0] < -- row 1
[0 2 -8 8] < -- row 2
[-4 5 9 -9] < -- row 3
When we do elementary row operations, say on row3 = row3 +...
A*z = 2z(xy+xz+yz)
V = xyz
x = V/yz
P/4 = x+y+z
P/4 - x - y = z
A*z = 2z(xy+xz+yz)
A( P/4 - x - y ) = 2(P/4 - x -y) ( V/z + V/y + yz )
is that right?
For a rectangular box, we could compute the area of one size and multiply by its depth
to get the volume no? I am...