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Unformatted text preview: MATH111 HW 4 Due Date: 8th Oct, 2007 (Mon) Please hand in your homework in my tutorial or putting it in the collection box outside MATH dept (Rm 3461, Lift 25-26) Ch2.3 # 8 Determine if the matrix 1 3 7 4 5 9 6 2 8 10 is invertible. Use as few calcula- tions as possible. Justify your answer. Ch2.3 # 12 The matrices in the following exercise are all n × n . Each part of the exercises is an implication of the form “If h statement 1 i , then h statement 2 i .” Mark an implication as True if the truth of h statement 2 i always follows whenever h statement 1 i happens to be true. An implication is False if there is an instance in which h statement 2 i is false but h statmenet 1 i is true. Justify each answer. a. If there is an n × n matrix D such that AD = I , then there is also an n × n matrix C such that CA = I . b. If the columns of A are linearly independent, then the columns of A span R n ....
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