Math254OldQuiz4 - Math 254 Name QUIZ 4 MATH 254 SUMMER 2001...

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Math 254 Name: ________________________ QUIZ 4 MATH 254 - SUMMER 2001 - KUNIYUKI CHAPTERS 7, 8 Show all appropriate work (as we have done in class) for full credit! A scientific calculator is allowed on this quiz. You do not have to rationalize denominators or simplify radicals (e.g., 12 2 3 = ). 1) Find the eigenvalues of A = - È Î Í ˘ ˚ ˙ 1 1 2 4 . (20 points)
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2) Diagonalize the matrix A = - È Î Í ˘ ˚ ˙ 2 2 1 5 by giving matrices P and D such that D P AP = - 1 , where D is diagonal. You do not have to give P - 1 . Hint: The eigenvalues of this matrix are 3 and 4. (30 points)
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3) The matrix A below is an orthogonal matrix. Write A - 1 , the inverse matrix. (5 points) A = - È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ 1 2 1 2 1 2 1 2 0 0 0 1 0 4) Let
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