Unless otherwise specified, you can use any known 
command to answer.You can check your answers after 
completion with any commands.

Do not look at the work other students are doing 
or communicate with anyone. I recommend that you 
SAVE regularly in case your computer crashes.

Try to work sequentially, making sure your commands 
give the shown responses, do NOT erase or correct 
lines, just redo your calculation on the next line 
if you get an error. You will not lose marks for errors.

To write comments in your worksheet use the # symbol, 
do this to put your name and registration number at 
the top of your worksheet:
> # James Preen  20152613

Use
> #  the answer is ... because
if any of your lines need further explanation. 

Save your work in your H:\ directory with your name 
somewhere in the filename and then please email the 
file to me at       james_preen@cbu.ca
Don't close Maple until you are sure I have the 
correct file. Once I have confirmed receipt you are 
free to leave. I will also have a flash drive too.


Please do not sit near your friends and leave a gap
between you and anyone else if possible. Using this 
diagram, identify which vectors you will be using: 


E F G H I     J A B C D 
=========     ========= 

I J A B C     D E F G H
=========     ========= 

C D E F G     H I J A B
=========     ========= 

G H I J A     B C D E F
=========     ========= 

A B C D E     F G H I J
=========     ========= 

 /
/door     screen

You have been allocated a particular set 
of 3 column vectors as below:

Vectors A
u:=<5,3,7>; v:=<6,6,7>; w:=<4,7,3>;

Vectors B
u:=<7,6,3>; v:=<2,4,5>; w:=<6,7,6>;

Vectors C
u:=<6,5,2>; v:=<5,2,7>; w:=<6,3,7>;

Vectors D
u:=<4,7,5>; v:=<6,2,7>; w:=<5,5,6>;

Vectors E
u:=<3,5,6>; v:=<2,4,5>; w:=<5,4,4>;

Vectors F
u:=<2,4,7>; v:=<7,5,7>; w:=<2,3,5>; 

Vectors G
u:=<6,3,5>; v:=<3,7,2>; w:=<5,4,4>; 

Vectors H
u:=<6,2,5>; v:=<7,4,6>; w:=<4,7,4>;

Vectors I
u:=<5,6,2>; v:=<5,7,3>; w:=<6,7,2>;

Vectors J
u:=<6,7,4>; v:=<4,5,5>; w:=<3,4,5>; 

Q0: 
Load the Maple package that contains the commands we need. [1 mark]

Q1:
(a) Form the following matrix using your vectors and use only
the command RowOperation on MI to find the inverse of M.  [8 marks]
> M:=<u|v|w>;
> MI:=<M|IdentityMatrix(3)>;
(b) Why do you now know that u, v and w are independent? [1 mark]

Q2:
Use the exact fit method to find the quadratic polynomial which 
has its x values stored in u and its y values in w. Check your 
answer by evaluating your polynomial at the x values. [6 marks]
(you do not need to use RowOperation this time; any method is ok)

Q3:
Using diagonalisation in reverse, or otherwise, create a 
3x3 matrix A with v as an eigenvector with eigenvalue 13. 
Multiply A and v to check you are correct. [4 marks]