06-240/Term Test

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==The Test==

===Front Page===

<center>

'''Do not turn this page until instructed.'''

<font style="font-size:150%">Math 240 Algebra I - Term Test</font>

University of Toronto, October 24, 2006

'''Solve the 5 problems on the other side of this page.'''

Each of the problems is worth 20 points.

You have an hour and 45 minutes.

'''Notes.'''

</center>

* No outside material other than stationary and a basic calculator is allowed.
* We will have an extra hour of class time in our regular class room on Thursday, replacing the first tutorial hour.
* The final exam date was posted by the faculty - it will take place on Wednesday December 13 from 2PM until 5PM at room 3 of the Clara Benson Building, 320 Huron Street (south west of Harbord cross Huron, home of the Faculty of Physical Education and Health).

<center> '''Good Luck!''' </center>

===Questions Page===

'''Solve the following 5 problems.''' Each of the problems is worth 20 points. You have an hour and 45 minutes.

'''Problem 1.''' Let <math>F</math> be a field with zero element <math>0_F</math>, let <math>V</math> be a vector space with zero element <math>0_V</math> and let <math>v\in V</math> be some vector. Using only the axioms of fields and vector spaces, prove that <math>0_F\cdot v=0_V</math>.

'''Problem 2.'''
# In the field <math>{\mathbb C}</math> of complex numbers, compute <center><math>\frac{1}{2 3i} \frac{1}{2-3i}</math>

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06-240/Term Test