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a5 - University of Toronto at Scarborough Department of...

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University of Toronto at Scarborough Department of Computer & Mathematical Sciences MATA33 Assignment 5 Winter 2008 Quiz 5 is based on this assignment and the relevant text readings and lecture notes. Quiz 5 will be written in the 6th tutorial, which takes place during the week of Feb. 25 - 29. Study: Lecture notes on determinants. A nice OnLine reference for determinants (and other topics on matrices) is http://distance-ed.math.tamu.edu/Math640/chapter1/node9.html Review our text and lecture material from Sections 6.1 -6.6 as necessary. Problems: 1. In all parts of this question, use the 2 × 2 matrices A and B in Example 4 on page 235. (a) Find det ( A ), det ( B ), and verify that det ( AB ) = det ( A ) det ( B ) and det ( A T ) = det ( A ) (b) Verify that det ( A + B ) 6 = det ( A ) + det ( B ) (c) Verify that det ( A - 1 ) = 1 det ( A ) (d) If C is the 2 × 2 matrix obtained by multiplying the first row of A by a number p and the second row of A by a number q , verify that det ( C ) = pq ( det ( A )). (e) Find all real numbers x for which the matrix xI - A is invertible. 2. In all of this question, use the 3 × 3 matrices A and B given at the beginning of the Problems Section 6.3 on page 248. (a) Find det ( A ), det ( B ), and then verify that det ( AB ) = det ( A ) det ( B ).
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