Math 111 21-22 Assignment 6
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Math 111 21-22
Assignment 6
Marks will be deducted for a solution of poor quality––neatness, order or readability. Scan your submission or take a high quality photo.
If you don’t have a dark pencil use a pen. In fact we highly recommend that you use a pen. First of all you should not be submitting a first draft. Secondly we would much much rather have a few boxes neatly crossed out than an entire document that we can hardly read. To take photos of your work, use lots of light and take care that each page is easily readable and is the right way up. Put your final answer in a box so that the marker can easily find it.
1. (5 marks) Find the solution to the dynamical system:
Write separate equations for 
, 
and 
in simplified form. I want you to solve this problem by hand so you have to show enough ofyour work to convince me youjust didn’t get technology to calculate the eigenvalues and eigenvectors.
2. (6 marks) (a) Calculate 
where 
Use your result to find 
10
.
(b) Let 
Calculate 
. Use your result to find 
10 .
For this question, express your answers in as simple a form as possible. Ifthe answer is an integer, provide the integer.
3. (5 marks) (a) At the right I give you a table of the factorials n! Define the sequence 
recursively as follows:
Sn = Sn−1 + n(n!) S1 = 1
Tabulate the first few terms of the sequence and compare what you get with the table of factorials. Use this to conjecture a simple general formula for 
(b) Use an inductive argument to show that your formula is correct. [Note: Take care with notation. Check everything. Try for a simple elegant presentation. Do not submit a first draft. Also you need to tell us what you are doing--not pull statements out of a hat. ]
2022-02-08