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Matrix Question

  1. Oct 12, 2004 #1

    JasonRox

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    I'm studying for a test and I got stuck here.

    Let A be the matrix:

    3..1
    2..1

    In each part find p(a).

    a) p(x)=x-2

    The answer is:

    1..1
    2..-1

    The only way I can see this happen is that we take the numbers on the diagonal and pluck it in p(x).

    So...
    x-2=3-2=1

    x-2=1-2=-1

    Leaving the others alone, we get.

    1..1
    2..-1


    The problem is, I know this is WRONG. This method does not work for b) and c), which are polynomials of higher degrees.

    The inverse is:

    1..-1
    -2..3

    I still can see a solution pattern.

    I tried to relate to the chapter, but no luck.

    Any help is appreciated.
     
  2. jcsd
  3. Oct 13, 2004 #2
    A matrix minus a scalar? That doesn't make any sense.
     
  4. Oct 13, 2004 #3

    matt grime

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    It is a matrix minus a scalar multiple of the identity matrix.
     
  5. Oct 13, 2004 #4

    JasonRox

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    Let's say I choose 2x-2.

    Would that be...

    4..1
    2..0

    If this is correct, would x^2 imply multiplying both matrixes.
     
  6. Oct 13, 2004 #5
    first of all do follow the standard notations ...
    we usually use capitals for matrices ...
    secondly
    2X - 2
    more often than not implies
    2X-2I
    where I is the identity matrix ...
    so u can see why the answer is the way it is .....

    and yes X^2 implies multiplication of matrices .... i.e X*X

    -- AI
     
  7. Oct 13, 2004 #6

    JasonRox

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    That's not what it says.

    The question doesn't have capitals and refers to the matrix as A.
     
  8. Oct 13, 2004 #7
    jason,
    it also asks u to find p(a)
    now this is really bad use of the notation actually.

    p(x) =x-2 is fine
    but i would expect them say
    find p(A) and not p(a)

    and yes when u sub in a matrix for x in an equation (in x) .. the constant (say c) is dealt as c*I ..

    -- AI
     
  9. Oct 13, 2004 #8

    JasonRox

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    I really appreciate your help.

    I understand where you are coming from. This might be the reason why I didn't know what was going on.
     
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