hw2soln - -V U )-1 V ) = I n-UV + U ( I m-V U )-1 V-UV U (...

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ECE 130C Homework 2 Solution April 20, 2007 1 . 5 . 4 L and U are " 1 0 4 1 # " 2 1 0 3 # ; 1 0 0 1 / 3 1 0 1 / 3 1 / 4 1 3 1 1 0 8 / 3 2 / 3 0 0 5 / 2 ; 1 0 0 1 1 0 1 1 1 1 1 1 0 3 3 0 0 4 . 1 . 5 . 18 Singular, no solution; Singular, infnitely many solutions; Non- singular, one solution. 1 . 5 . 40 (3 , 1 , 2 , 4) and (2 , 3 , 1 , 4) keep only 4 in position; six more even P ’s keep 1 or 2 or 3 in position; (2 , 1 , 4 , 3) and (3 , 4 , 1 , 2) exchange two pairs. Then (1 , 2 , 3 , 4) and (4 , 3 , 2 , 1 make a total oF twelve even P ’s. 1 . 5 . 42 P 1 P 2 = 0 1 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 6 = P 2 P 1 . P 3 P 4 = 0 1 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 = P 4 P 3 . 1 . 6 . 4 (a) A - 1 AB = A - 1 AC B = C . (b) " 1 0 0 0 # " 1 0 0 2 # = " 1 0 0 0 # " 1 0 0 3 # . 1 . 6 . 8 Ax = 0 For x = " - 1 1 # ; AB = I is not solvable. 1 . 6 . 18 All oF e, f, c must be nonzero; e and ad - bc must be nonzero. 1
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1 . 6 . 20 A - 1 = 1 0 0 0 - 1 / 4 1 0 0 - 1 / 4 - 1 / 3 1 0 - 1 / 4 - 1 / 3 - 1 / 2 1 . 1 . 6 . 44 The solution is x = (1 , 1 , . . . , 1): all ones. 1 . 6 . 48 MM - 1 = ( I n - UV )( I n + U ( I m
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Unformatted text preview: -V U )-1 V ) = I n-UV + U ( I m-V U )-1 V-UV U ( I m-V U )-1 V = I n-UV + U ( I m-V U )( I m-V U )-1 V = I n 3 . a + d = 0; a + e =-1; a + f =-2 3 a + ( d + e + f ) =-3 (1) similarly, we can get 3 b + ( d + e + f ) = 0 (2) and, 3 c + ( d + e + f ) = 3 (3) then (3)-(1), we get c-a = 2 a = c-2 (3)-(2), we get c-b = 1 b = c-1 Also, we know that c + d = 2; c + e = 1; c + f = 0. So d = 2-c e = 1-c f =-c 2...
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hw2soln - -V U )-1 V ) = I n-UV + U ( I m-V U )-1 V-UV U (...

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