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Math Help - Describe the position of the elements of a matrix.

  1. #1
    kkm
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    Describe the position of the elements of a matrix.

    Given this problem:

    In the square matrix «afj» of order two describe the position of the
    elements. Where:
    (a) i = 2
    (b) j = 1
    (c) i = j

    This is an excerpt from my maths book. I do not understand what I exactly have to to do. Can you assist me with this one, please?
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  2. #2
    A Plied Mathematician
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    Are you sure it's afj, or is it more like A_{ij}? Does square matrix of order two mean that it's a 2 x 2 matrix?
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  3. #3
    kkm
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    Thumbs up

    Yes, the matrix is A_{ij}.

    Yes, square matrix of order two means it's a 2 x 2 matrix.

    Sorry for the confusion.
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  4. #4
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    So, you tell me, what does the i correspond to? And what does the j correspond to?
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  5. #5
    kkm
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    Quote Originally Posted by Ackbeet View Post
    So, you tell me, what does the i correspond to? And what does the j correspond to?
    i refers to the matrix' row index.
    j refers to the column index.

    Still, I don't seem to understand the exercise. Thanks, for your time.
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  6. #6
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    So, which elements of the following matrix A have row index = 2?

    A=\left[\begin{matrix}2 &5\\7 &3\end{matrix}\right].
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  7. #7
    kkm
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    Quote Originally Posted by Ackbeet View Post
    So, which elements of the following matrix A have row index = 2?

    A=\left[\begin{matrix}2 &5\\7 &3\end{matrix}\right].
    I think I know what you're trying to say and I will try to solve the exercise.

    So, given your matrix, the solution to a would be:

    A_{21} with element 7
    A_{22} with element 3

    To b:

    A_{12} with element 5
    A_{22} with element 7

    To c:

    A_{11} with element 2
    A_{12} with element 5

    Am I right?
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  8. #8
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    For part a, you have correctly exhibited the elements there. How would you describe where those elements are in the matrix?

    You should double-check your answer for parts b and c.
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  9. #9
    kkm
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    Quote Originally Posted by Ackbeet View Post
    For part a, you have correctly exhibited the elements there. How would you describe where those elements are in the matrix?

    You should double-check your answer for parts b and c.
    I would say: "The elements are in the second row of the matrix A with order 2 x 2."

    Correction

    A=\left[\begin{matrix}2 &5\\7 &3\end{matrix}\right].

    b) where j = 1:
    A_{11} with element 2
    A_{21} with element 7

    I must have slept to get this wrong...

    The position of the elements would be: "the second column of the matrix A with order 2 x 2".

    c where i = j, so i = 1:

    A_{11} with element 2
    A_{12} with element 5

    Why, isn't this right?

    Or, does it mean where i = 1 and where j = 1?

    Then, of course, it would be:

    A_{11} with element 2

    The position would be: "the first column and row of the matrix A with order 2 x 2".

    Is this right? I hope I am beginning to understand...
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  10. #10
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    You've nailed part a. I think a statement such as "The elements are in the second row of the matrix A with order 2 x 2." is precisely what the problem is asking for. For part b, you've got the right idea, but not the correct details. It's not the second column, but the _______ column.

    For part c, i=j by no means forces i to equal 1. What if i=j=2? So which matrix elements are those?
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  11. #11
    kkm
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    Quote Originally Posted by Ackbeet View Post
    You've nailed part a. I think a statement such as "The elements are in the second row of the matrix A with order 2 x 2." is precisely what the problem is asking for. For part b, you've got the right idea, but not the correct details. It's not the second column, but the _______ column.
    Oh, yes. Of course, it's the first column. My head must be somewhere, but not with me.

    For part c, i=j by no means forces i to equal 1. What if i=j=2? So which matrix elements are those?
    You're right. My presumption was false.

    A_{11} and
    A_{22} because i = j.

    The position of the elements would be: "the row and column where the value of the row index equals the column index."
    After writing it down it makes much more sense to me.

    Oh, yes, I hope I get it right now.
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  12. #12
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    Everything looks good. There is a name for the elements described by part c: the main diagonal. I think that's what the problem is after there.
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  13. #13
    kkm
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    Quote Originally Posted by Ackbeet View Post
    Everything looks good. There is a name for the elements described by part c: the main diagonal. I think that's what the problem is after there.
    OK.

    Sorry for bothering you about this, but my Math book had no "Solutions"-part, where I could easily have looked it up.
    Thanks again, Ackbeet, for your valuable help and enormous patience over me. I would really consider donating you money for your help, but I think I have to put that on my Someday list, because I'm a poor student from Paraguay.
    The advice for writing things down is an excellent one, which I'll must keep in mind, but it was essentially part of the exercise.

    Goodbye
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  14. #14
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    You're very welcome. Have a good one!
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