NE112-quiz3

# NE112-quiz3 - A = 0 10 If det A = 7 then A is invertible...

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NE112 – Linear Algebra Quiz # 2 Student Name: Student Number: For questions 1 to 10, answer whether each statement is True (T) or False (F) 1. The vector - 6 2 is a linear combination of - 4 3 and 2 1 . 2. If 2 u - 3 v = 4 w - 2 v + 2 u , then w is a linear combination of u and u + v . 3. If a , b , and c are vectors with a orthogonal to b , then ( a.b ) c = a ( b.c ), for any c . 4. a. ( b + c ) = c.a + b.a , for all vectors a , b , and c in R n . 5. The angle θ between the vectors u = (-5, -1, 1) and v = (2, 4, -4) is approximately 125 o .

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6. The minor m 21 in - - - - 2 1 2 1 2 3 1 0 3 2 0 1 0 5 1 3 is -2. 7. If B is formed by adding a linear combination of two rows of A to a different row of A , then det( B ) = det( A ). 8. The determinant of any square triangular matrix is nonzero. 9. If A has two columns equal, then det(

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Unformatted text preview: A ) = 0. 10. If det( A ) = 7, then A is invertible and so is A T . 11. If i h g f e d c b a = 3, then c f c i b e b h a d a g 2 4 2 4 2 4---is A. 6 B. -12 C. -24 D. 12 E. 24 F. -6 12. Which of the vectors below is orthogonal to both (2, 1, -1) and (-3, -2, 4)? A. (2, -5, -1) B. (1, 0, 1) C. (-4, 0, 3) D. (1, -2, 0) E. (3, 0, 2) F. None of the above 13. If u = (-2, 1, 1) and v = (1, 0, 1) then u v proj is A. 0 B. 1/2 C. 2 / 2 D. 1 E. 6 / 6 F. 1/6 14. The value of 1 1 2 1 3 2 1 4 3 2 1 4 3 2 is A. B. 1 C. 2 D. 7 E. -3 F. -7 15. Find ξ so that the value of 1 2 1 3 2 4 3 2 1 4 3 2 ξ is 5. A. 5 B. 0 C. 5/2 D. 2/5 E. 5/7 F. 7/5...
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## This note was uploaded on 10/08/2010 for the course NE 112 taught by Professor Vanelli during the Spring '10 term at Waterloo.

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NE112-quiz3 - A = 0 10 If det A = 7 then A is invertible...

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