Math254Mid1

Math254Mid1 - Math 254 Name MIDTERM 1 MATH 254 SUMMER 2002...

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Math 254 Name: ________________________ MIDTERM 1 MATH 254 - SUMMER 2002 - KUNIYUKI CHAPTERS 1, 2, 3 GRADED OUT OF 75 POINTS ¥ 2 = 150 POINTS TOTAL Circle your final answers! Show all work and simplify wherever appropriate, as we have done in class! 1) Use either Gaussian elimination with back-substitution or Gauss-Jordan elimination to solve the following system. You must use matrices, as we have done in class. Write your answer as an ordered triple of the form xxx 123 ,, () . 441 45 0 31 2 9 0 39 12 3 23 3 xx x x -+ = += = Ï Ì Ô Ô Ó Ô Ô (15 points)
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2) Consider the system xx x 12 4 34 26 37 +- = += Ï Ì Ô Ó Ô (10 points total) a) Write the solution set of the system in parametric form, as we have done in class. b) Use part a) to find two particular solutions to the system. Note: There are infinitely many possible answers.
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3) Find the matrix product AB T where A =- È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 2 1 0 0 4 1 and B = - - È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 1 0 1 2 3 0 0 2 0 . (6 points) 4) Find the inverse of the matrix 020 004 300 È Î Í Í Í ˘ ˚ ˙ ˙ ˙ (6 points)
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5) Let A be the matrix 201 41 3 04 1 -- - È Î Í Í Í ˘
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Math254Mid1 - Math 254 Name MIDTERM 1 MATH 254 SUMMER 2002...

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