Test 2 Solutions

# Test 2 Solutions - Test 2 SOLUTION MATH1104B Fall 2009 Last...

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MATH1104 B , Fall, 2009 Last name: First name: Student no.: ———————————————————————————————————– 1-[10 marks]: Let T : R n -→ R m is deﬁned by : T x y z w = x + z y + z y + 2 w . a) What is n and m ? b) Find T (2 , 1 , - 1 , 1) . c) Find A T the standard transformation matrix of T . d) Is T one-to-one? Justify your answer. e) Is T onto? Justify your answer. Solution: (a): n = 4 , m = 3 (b): (1 , 0 , 3). (c): By ﬁnding T ( e i ) ,i = 1 , 2 , 3 , 4, A T = 1 0 1 0 0 1 1 0 0 1 0 2 . (d): An REF form of A T is B = 1 0 1 0 0 1 1 0 0 0 - 1 2 . Since A T has no pivot in every column (the 4th column is not pivot) then T in NOT one-to-one. (d): Since A T has pivot in each row, then T is onto. 1

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Test 2 Solutions - Test 2 SOLUTION MATH1104B Fall 2009 Last...

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