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Week of...
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Notes and Links
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1
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Sep 10
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About This Class, Tuesday, Thursday
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2
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Sep 17
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HW1, Tuesday, Thursday, HW1 Solutions
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3
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Sep 24
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HW2, Tuesday, Class Photo, Thursday
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4
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Oct 1
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HW3, Tuesday, Thursday
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5
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Oct 8
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HW4, Tuesday, Thursday
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6
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Oct 15
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Tuesday, Thursday
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7
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Oct 22
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HW5, Tuesday, Term Test was on Thursday. HW5 Solutions
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8
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Oct 29
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Why LinAlg?, HW6, Tuesday, Thursday, Nov 4 is the last day to drop this class
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9
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Nov 5
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Tuesday, Thursday
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10
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Nov 12
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Monday-Tuesday is UofT November break, HW7, Thursday
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11
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Nov 19
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HW8, Tuesday,Thursday
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12
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Nov 26
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HW9, Tuesday , Thursday
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13
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Dec 3
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Tuesday UofT Fall Semester ends Wednesday
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F
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Dec 10
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The Final Exam (time, place, style, office hours times)
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Register of Good Deeds
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Add your name / see who's in!
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Problem. Find the rank the matrix
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Solution. Using (invertible!) row/column operations we aim to bring to look as close as possible to an identity matrix:
Do
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Get
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Do
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Get
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1. Bring a to the upper left corner by swapping the first two rows and multiplying the first row (after the swap) by .
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2. Add times the first row to the third row, in order to cancel the in position 3-1.
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3. Likewise add times the first row to the fourth row, in order to cancel the in position 4-1.
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4. With similar column operations (you need three of those) cancel all the entries in the first row (except, of course, the first, which is used in the canceling).
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5. Turn the 2-2 entry to a by multiplying the second row by .
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6. Using two row operations "clean" the second column; that is, cancel all entries in it other than the "pivot" at position 2-2.
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7. Using three column operations clean the second row except the pivot.
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8. Clean up the row and the column of the in position 3-3 by first multiplying the third row by and then performing the appropriate row and column transformations. Notice that by pure luck, the at position 4-5 of the matrix gets killed in action.
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Thus the rank of our matrix is 3.