201_2016_2_b

# Select from the following 1 only a and b 2 only a 3

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Select from the following: 1. Only A and B. 2. Only A. 3. Only B. 4. Only B and C. 5. None of the above. Answer: 4 First consider the matrices in M 22 which belong to X : a b c d 1 1 = 0 0 a + b c + d = 0 0 a + b = 0 , c + d = 0 b = - a, d = - c so that X = a - a c - c : a, c R = a 1 - 1 0 0 + c 0 0 1 - 1 : a, c R = span 1 - 1 0 0 , 0 0 1 - 1 . Since 1 - 1 0 0 , 0 0 1 - 1 is a linearly independent set, and spans X , B provides a basis for X . Since every basis for X must have the same number of elements, A does not describe a basis for X . Question 5 Which of the following statements are true: 5
Select from the following: 1. All of A, B, C and D. 2. Only B. 3. Only A and B. 4. Only A and C. 5. None of the above. Answer: 5
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