math1104 exam

# math1104 exam - 1 2-3-1 2 5 1 Let A =-1 3 1 and let B = 4-2...

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1. Let A = 12 3 13 1 42 5 and let B = 5 3 4 21 6 32 . What is the third column of AB . a) 2 1 7 b) 8 2 4 c) 2 8 4 d) 13 8 2 21 2. Let A = 13 132 2 2 and let B = 5 3 4 6 3 2 2 1 . What is the second row of AB . a) 10 10 8 8 b) 10 10 10 10 c) 15 402 3 d) 7 2 4 3. Consider the following augmented matrix of a system of linear equations. 11 22 3 10 3 3 4 1 k 4 For what value(s) of k the system has in±nitely many solutions? a) There is no value of k for which the system has in±nitely many solutions. b) For k = 2 the system has in±nitely many solutions. c) k = 2 the system has in±nitely many solutions. d) For every real number k , the system has in±nitely many solutions. 4. Consider the following augmented matrix of a system of linear equations. 14 6 1 01 7 7 00 k 2 64 k +8 . Which of the following statements is TRUE? a) There is a unique solution when k = 8. b) There are in±nitely many solutions for k = 8. c) There is no value of k for which there is a unique solution. d) There is a unique solution when k =8. 5. Find all the values of k for which the system with the following augmented matrix is consistent: ± 1 5 4 0( k +3)( k 8) ( k k 5) ² . a) k 6 = 3 b) k 6 =8 c) k d) k = 3 , 8

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6. Consider the following augmented matrix of a system of linear equations: 11 22 3 1 2 3 10 3 2 2 3 . Which of the following statements is TRUE? a) The system has a unique solution b) The system has inFnitely many solutions with one parameter c) The system has inFnitely many solutions with two parameters d) The system has no solutions 7. Consider the matrix equation 122 254 36 k x y z = h 7 9 . The above matrix equation has a UNIQUE solution if a) k =6and h 6 =3 b) ±or all k in R and h 6 =3. c) k 6 = 6 and for all h in R . d) k h 8. Let v 1 = 1 0 0 , v 2 = 2 1 0 , v 3 = 1 1 2 , v 4 = 5 4 8 . Which of the following statements is TRUE? a) v 3 is in Span { v 1 ,v 2 } b) v 4 is in Span { v 1 2 } c) v 1 is in Span { v 2 3 } d) v 4 is in Span { v 1 3 } 9. Let v 1 = 1 1 1 2 , v 2 = 2 3 2 4 , v 3 = 1 2 3 2 , v 4 = 5 1 3 h . ±or what value(s) of h the vector v 4 is in Span { v 1 2 3 } ? a) h = 10. b) h = 10. c) There is no value of h for which the vector v 4 is in Span { v 1 2 3 } . d) ±or every real number h , the vector v 4 is in Span { v 1 2 3 } .
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math1104 exam - 1 2-3-1 2 5 1 Let A =-1 3 1 and let B = 4-2...

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