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Week of...
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Notes and Links
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1
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Sep 11
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About, Tue, HW1, Putnam, Thu
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2
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Sep 18
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Tue, HW2, Thu
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3
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Sep 25
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Tue, HW3, Photo, Thu
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4
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Oct 2
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Tue, HW4, Thu
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5
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Oct 9
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Tue, HW5, Thu
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6
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Oct 16
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Why?, Iso, Tue, Thu
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7
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Oct 23
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Term Test, Thu (double)
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8
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Oct 30
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Tue, HW6, Thu
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9
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Nov 6
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Tue, HW7, Thu
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10
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Nov 13
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Tue, HW8, Thu
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11
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Nov 20
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Tue, HW9, Thu
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12
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Nov 27
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Tue, HW10, Thu
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13
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Dec 4
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On the final, Tue, Thu
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F
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Dec 11
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Final: Dec 13 2-5PM at BN3, Exam Forum
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Register of Good Deeds
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Add your name / see who's in!
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edit the panel
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The Test
Front Page
Do not turn this page until instructed.
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 be a field with zero element , let be a vector space with zero element and let be some vector. Using only the axioms of fields and vector spaces, prove that .
Problem 2.
- In the field {\mathbb C} of complex numbers, compute and .
- Working in the field of integers modulo 7, make a table showing the values of for every .
Problem 3. Let be a vector space and let and be subspaces of . Prove that is a subspace of iff or .
Problem 4. In the vector space , decide if the matrix is a linear combination of the elements of .
Problem 5. Let be a finite dimensional vector space and let and be subspaces of for which . Denote the linear span of by . Prove that .
Good Luck!
Solution Set
Students are most welcome to post a solution set here.
1. (by F3)
(by VS8)
By VS4,
Add to both sides of
(by construction)
(by VS3)
2. 1)
2)