MAT 272 Assignment 4 - solutions

# MAT 272 Assignment 4 - solutions - simplifies to x b 1 b 2...

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MAT 272 Assignment #4 Due: October 15, 2009 1) Calculate the following determinants using cofactor expansion. Show your work. a.

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b. 2) Let A = and k = -2. Verify that det( k A) = k 3 det(A). (-2)A = det(-2A) = -448 (-2)3det(A) = (-8)det(A) = -448.
3) Let A = . Verify that det(A) = det(A T ). det(A) = 15 A T = det(A T ) = 15 4) Given that . Calculate the following: a. This is the result if two row interchanges R1↔R2 followed by R2↔R3. The answer is b. This is the result of the row operations 3R1→R1, -1R2→R2 and 4R3→R3. c. This is the result of the row operation R1+R3→R1. There is no effect on the determinant.

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5) Prove that the equation of the line through the distinct points and can be written as .
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Unformatted text preview: simplifies to x( b 1- b 2 ) – y( a 1 – a 2 ) + a 1 b 2 – b 1 a 2 = 0. Separating the variables leads to x ( b 1- b 2 ) + a 1 b 2 – b 1 a 2 = y ( a 1 – a 2 ) x ( b 1- b 2 ) + a 1 b 2 = y ( a 1 – a 2 ) + b 1 a 2 add b 1 a 2 to both sides x ( b 1- b 2 ) + a 1 b 2- b 1 a 1 = y ( a 1 – a 2 ) + b 1 a 2- b 1 a 1 subtract b 1 a 1 from both sides x ( b 1- b 2 ) – a 1 (b 1 – b 2 ) = y ( a 1 – a 2 ) – b 1 (a 1- a 2 ) factor (x – a 1 ) ( b 1- b 2 ) = ( y – b 1 ) ( a 1 – a 2 ) factor divide both sides by ( a 1 – a 2 ) Alternately, you can substitute the equation of the line into the determinant and simplify as follows:...
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MAT 272 Assignment 4 - solutions - simplifies to x b 1 b 2...

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