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math3c-01-W08..

# math3c-01-W08.. - ±ned For those de±ned enter the size of...

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26. (1 pt) - 7 - 3 - 1 0 1 - 2 - 28 - 12 - 6 Compute the rank of the above matrix 27. (1 pt) 7 4 7 7 4 3 21 12 17 Compute the rank of the above matrix 28. (1 pt) 3 x - 1 y + 9 z = 5 6 x + 3 y + 6 z = 4 8 x + 5 y + 9 z = 4 Write the above system of equations in matrix form: * x y z = 29. (1 pt) If A = - 4 4 3 4 - 2 - 2 0 2 3 and B = - 1 - 2 - 1 - 3 - 3 - 4 0 2 - 2 Then 4 A + B = and A T = 30. (1 pt) If A = - 2 - i 4 i - 3 + i and B = 3 + 3 i - 2 - 2 i 1 + i Then AB = and BA = 31. (1 pt) Let M = 5 4 3 5 . Find c 1 and c 2 such that M 2 + c 1 M + c 2 I 2 = 0, where I 2 is the identity 2 × 2 matrix. c 1 = , c 2 = . 32. (1 pt) Let M = - 2 - 1 - 2 - 2 3 3 - 2 2 1 . Find c 1 , c 2 , and c 3 such that M 3 + c 1 M 2 + c 2 M + c 3 I 3 = 0, where I 3 is the identity 3 × 3 matrix. c 1 = , c 2 = , c 3 = . 33. (1 pt) Compute the following product. ( 1 - 1 - 3 ) - 3 - 1 - 2 - 2 - 3 2 = ( ) 34. (1 pt) If A , B , and C are 2 × 2 , 2 × 7 , and 7 × 9 matrices respectively, determine which of the following products are de-
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Unformatted text preview: ±ned. For those de±ned, enter the size of the resulting matrix (e.g. ”3 x 4”, with spaces between numbers and ”x”). For those unde±ned, enter ”unde±ned”. AB : BC : AC : BA : 35. (1 pt) Find the ranks of the following matrices. rank -8 5 = rank -5 7 8 = rank ± 1 5 7 ² = 36. (1 pt) Find a and b such that 28 8-6 = a 1 1-2 + b 6 2-2 . a = b = Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c ± UR 3...
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