06-240/Term Test

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The Test

Front Page

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Math 240 Algebra I - Term Test

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.

• 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).

Good Luck!

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]\displaystyle{ F }[/math] be a field with zero element [math]\displaystyle{ 0_F }[/math], let [math]\displaystyle{ V }[/math] be a vector space with zero element [math]\displaystyle{ 0_V }[/math] and let [math]\displaystyle{ v\in V }[/math] be some vector. Using only the axioms of fields and vector spaces, prove that [math]\displaystyle{ 0_F\cdot v=0_V }[/math].

Problem 2.

1. In the field [math]\displaystyle{ {\mathbb C} }[/math] of complex numbers, compute [math]\displaystyle{ \frac{1}{2 3i} \frac{1}{2-3i} }[/math]