test2a - Version 1 1 Solutions to Test 2 - MATH 1104F -...

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Unformatted text preview: Version 1 1 Solutions to Test 2 - 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. The standard matrix for the linear transformation T : R 2 R 2 that represents a reflection through the x-axis (or x 1-axis) is ( a ) 1- 1 ( b )- 1- 1 ( c )- 1 0 0 1 ( d )- 1- 1 Solution: (a) 2. The inverse of 2- 3- 2 6 is ( a ) 6 3 2 2 ( b )- 1 1 3 / 2- 3 ( c ) 1 / 3- 1 / 2- 1 / 3 1 ( d ) 1 1 / 2 1 / 3 1 / 3 Solution: (d) 3. Which of the following statements are true? (i) Let T : R 3 R 3 be a linear transformation. If T is one-to-one then T is onto. (ii) If T : R n R m is one-to-one then n m . (iii) The transformation T : R 2 R 3 defined by T ( x,y ) = ( x + 1 ,y + 1 , 1) is linear. (iv) Let A , B and C be n n matrices. Then ( AB- 1 + C ) T = A T ( B- 1 ) T + C T ....
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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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test2a - Version 1 1 Solutions to Test 2 - MATH 1104F -...

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