Answer:
I.
A is a 4 x 5 matrix => A: U -> V, dim U = 5, dim V = 4
Null space is exactly two dimensional plane
dim null (A) = 2
II.
Rank A = dim U - dim Null A = 5 - 2 = 3
III.
Number of linearly Independent columns of A is the rank of A = 3
IV.
Yes, The system Ax = b has no solution sometimes as range of A \neq V
V.
Yes,Sometimes Ax = b has a unique solution
VI.
Yes, sometimes Ax = b has infinitely many solutions
<h2>
Hello!</h2>
The answer is:
In 2036 there will be a population of 32309 rabbits.
<h2>
Why?</h2>
We can calculate the exponential decay using the following function:

Where,
Start Amount, is the starting value or amount.
Percent, is the decay rate.
t, is the time elapsed.
We are given:

Now, substituting it into the equation, we have:






Hence, we have that in 2036 the population of rabbis will be 32309 rabbits.
Have a nice day!