2107test2_09

2107test2_09 - MATH 2107A TEST 2 This test has for pages...

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MATH 2107A TEST 2 OCTOBER 23, 2009 1 of 4 This test has for pages with a total of 30 marks. Show all your work. The test cannot be taken out from the examination room. Only nonprogrammable calculators are allowed. Duration: 50 minutes. NAME (in ink): STUDENT NO (in ink): [ 6] 1. Find a linear transformation 2 : P T with the following properties; 2 ) 2 ( = + x T , 1 ) 1 ( = T , 1 ) ( 2 = + x x T . Compute ) 2 3 ( 2 + x x T

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MATH 2107A TEST 2 OCTOBER 23, 2009 2 of 4 [9] 2. Let 4 3 : T ;) 4 3 , 2 , , 2 ( ) , , ( z y x z x z y x z y x z y x T + + + + = be a linear transformation. (a) Find ) ker( T and a basis 1 B of ) ker( T . (b) Find a basis B of 3 that includes the vectors in 1 B . (c) Construct a basis of ) ( T im using the appropriate vectors in B .
MATH 2107A TEST 2 OCTOBER 23, 2009 3 of 4 [6] 3. Let 3 2 : T ;) 2 , , ( ) , ( b a b a b a T + = be a linear transformation. (a) Find

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2107test2_09 - MATH 2107A TEST 2 This test has for pages...

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