test3a - Version 1 1 Solutions to Test 3 - MATH 1104F -...

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Version 1 1 Solutions to Test 3 - MATH 1104F - Winter 2010 Version 1 PART I: Multiple choice questions (3 points each) Choose and circle only one answer. No partial marks here. No justification is required. 1. Let T : R 2 R 2 be the linear transformation given by T ( x,y ) = ( y, - x ). Then the inverse of T is: ( a ) T - 1 ( x,y ) = ( - x,y ) ( b ) T - 1 ( x,y ) = ( x, - y ) ( c ) T - 1 ( x,y ) = ( - y,x ) ( d ) T - 1 ( x,y ) = ( - y, - x ) Solution: (c) 2. Let S 1 = Span { (1 , 0 , - 1) , (2 , - 1 , 1) } , S 2 = Nul 1 0 1 0 1 1 1 1 0 , S 3 = { (1 , 2 , 0) , ( - 1 , 1 , 0) } , and S 4 = { ( a + b,a - b, 1): a and b are real numbers } . The following are subspaces of R 3 : ( a ) S 1 and S 2 only ( b ) S 1 and S 4 only ( c ) S 2 and S 3 only ( d ) S 3 and S 4 only Solution: (a) 3. Let A be an n × n matrix. Consider the following statements: (i) A is an invertible matrix. (ii) The columns of
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This note was uploaded on 03/22/2010 for the course MATH 1104 taught by Professor Unknown during the Winter '10 term at Carleton.

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test3a - Version 1 1 Solutions to Test 3 - MATH 1104F -...

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