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Matrix question

  1. Jul 6, 2010 #1
    1. The problem statement, all variables and given/known data
    Use the matrix capabilities of a graphing utility to find:


    2. Relevant equations

    3. The attempt at a solution

    Well, I know the answer is
    However, I don't know how to get it.

    I would think you would do A^2-5A+2 however you cant add a constant to a matrix. I'm not sure exactly what I'm supposed to do.
  2. jcsd
  3. Jul 6, 2010 #2
    The constant 2 might be
  4. Jul 6, 2010 #3
    Nope, thats not it. Just tried it and it's wrong, not sure how it would be it though.
  5. Jul 6, 2010 #4
    A constant by itself might signify that it is in operation with an identity. So 2 might be


  6. Jul 6, 2010 #5
    oh, ok. That's turns out to be right. Thanks!
  7. Jul 6, 2010 #6


    Staff: Mentor

    Right. The polynomial is f(A) = A2 - 5A + 2I.
  8. Jul 6, 2010 #7
    How exactly did you derive 'I's value?
  9. Jul 6, 2010 #8


    Staff: Mentor

    I is the 2 x 2 identity matrix, defined as

    Since A is given as a 2 x 2 matrix, the appropriate identity matrix must also be 2 x 2. If A were given as a 3 x 3 matrix, you would need to use the 3 x 3 identity matrix, which is defined as

    The form of the identity matrix to use depends on the size of the square matrices being used in the problem.
  10. Jul 6, 2010 #9
    Ahh.. ok. I didn't know what an identity matrix was before. But now I know. Interesting.
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