mat1302-practice-midterm2-solutions

# mat1302-practice-midterm2-solutions - MATH 1302 PRACTICE...

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MATH 1302 - PRACTICE SECOND MIDTERM EXAM SOLUTIONS WINTER 2008 1. Let A = 3 7 - 1 0 4 - 8 , B = 1 2 1 / 2 - 8 0 0 3 2 / 3 5 , C = 2 0 1 - 1 3 4 , D = 2 8 - 4 0 3 4 a) Which of the following operations are deﬁned? AB, BA, AC, CA, AD, DA For those that are deﬁned, what is the size of the resulting matrix? Answer: BA , AD and DA are not deﬁned because the sizes do not match. AB is deﬁned and is a 2 × 3 matrix. AC is deﬁned and is a 2 × 2 matrix. CA is deﬁned and is a 3 × 3 matrix. b) Which of the following operations are deﬁned? A + B, A + D, A + D + B, 2 A - D For those that are deﬁned, what is the result? Answer: A + B and A + D + B are not deﬁned. The other operations are deﬁned and A + D = 5 15 - 5 0 7 - 4 , 2 A - D = 4 6 2 0 5 - 20 c) What are A T and B T ? Answer: A T = 3 0 7 4 - 1 - 8 , B T = 1 - 8 3 2 0 2 / 3 1 / 2 0 5

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2 MAT 1302 - PRACTICE SECOND MIDTERM EXAM SOLUTIONS 2. a) Suppose A is a 6 × 8 matrix and the product AB T is deﬁned and is a 6 × 10 matrix. What is the size of
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mat1302-practice-midterm2-solutions - MATH 1302 PRACTICE...

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