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M235A2

# M235A2 - MATH 235 Determinants Assignment 2 Hand in...

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MATH 235 Determinants Assignment 2 Hand in questions 1,6,8,10,15 by 9:30 am on Wednesday September 27, 2006. 1. Evaluate the determinants of the following matrices: ( a ) 2 - 1 6 7 2 - 5 - 3 1 4 , ( b ) 1 2 3 0 2 6 6 1 - 1 0 0 3 0 2 0 5 , ( c ) 2 - 1 0 0 0 - 1 2 - 1 0 0 0 - 1 2 - 1 0 0 0 - 1 2 - 1 0 0 0 - 1 1 , ( d ) A n × n = a b b · · · b b a b · · · b b b a · · · b . . . . . . . . . . . . . . . b b b · · · a . 2. Find all values of x R , z C for which the following matrices are invertible: ( a ) cos x 1 - sin x 0 2 0 sin x 3 cos x , ( b ) 1 1 x 1 x x x x x , ( c ) 1 + i 3 - 2 i 1 - i 2 - i 2 z 2 i - 1 - i 2 z . 3. Show that the equation of the line in R 2 through distinct points ( x 1 , y 1 ) and ( x 2 , y 2 ) can be written as det 1 x y 1 x 1 y 1 1 x 2 y 2 = 0 . 4. Let A, B, C and D be n × n matrices with A invertible. (a) Find matrices X and Y to produce the block LU factorization A B C D = I O X I A B O Y and show that det A B C D = det( A ) det( D

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M235A2 - MATH 235 Determinants Assignment 2 Hand in...

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