1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix Question

  1. Oct 12, 2004 #1

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper

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

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Homework Helper
    Gold Member

    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

    User Avatar
    Homework Helper
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Matrix Question
  1. Matrix question (Replies: 2)

Loading...