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Matrix maybe it can go in precalc section ?

  1. Aug 14, 2013 #1
    1. The problem statement, all variables and given/known data

    Let A and B be matrices of the same size.
    a.) prove the jth column of ## A + B## is ## a_j + b_j ##

    2. Relevant equations

    Where is i? In their question?

    3. The attempt at a solution
    What if you did this.

    ##
    A=
    \begin{pmatrix}
    a_{1j}\\
    a_{2j}\\
    a_{3j}
    \end{pmatrix}
    ##

    B = ##
    \begin{pmatrix}
    b_{1j}\\
    b_{2j}\\
    b_{3j}
    \end{pmatrix}
    ##

    A+B = ##
    \begin{pmatrix}
    a_{1j} + b_{1j}\\
    a_{2j} + b_{2j}\\
    a_{3j} + b_{3j}
    \end{pmatrix}
    ##

    But I still have i and they say prove that it is aj + bj
    I hope that code is right for the matrix when I preview it is would not show. EDIT Why does my code not work ?
     
    Last edited by a moderator: Aug 14, 2013
  2. jcsd
  3. Aug 14, 2013 #2

    SteamKing

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    IMO, the question assumed that since the jth column of A + B was sought, it was naturally implied the index i would range from 1 ... n, where n is the number of rows in A and B.
     
  4. Aug 14, 2013 #3
    What is IMO. Am I correct or no?
     
  5. Aug 14, 2013 #4

    rcgldr

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    Is this proof meant to be done with a computer program, or is it just a proof? If it's just a proof, it's not clear what is being sought here, there's a definition for adding matrices, and the syntax aj means all values (all rows) in column j of the matrix A, and bj means all values in column j of B. You do not need to define an "i", unless you're trying to create a program, depending on the programming language.

    In a language called APL, indexes for a multi-dimension array are separated by ';', and an empty field means all of the indexes for that dimension. So in APL, aj => A[ ; j ], and bj => B[ ; j ], no "i" needed. For example:

    pf3.jpg
     
    Last edited: Aug 14, 2013
  6. Aug 14, 2013 #5
    No program just what the question says prove that Let A and B be matrices of the same size.
    a.) prove the jth column of A+B is aj+bj

    So I just put them in matrices and added them to show that yeah it is aj + bj ...I mean idk that is what the question said exactly
     
  7. Aug 14, 2013 #6

    rcgldr

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    I'm not sure what constitutes "proof" since the statement is true based on the definitions of A+B and aj + bj.
     
  8. Aug 14, 2013 #7
    Yeah I'm not sure I guess they wanted you to carry out the operation? I suppose.
     
  9. Aug 14, 2013 #8

    D H

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    I fixed it for you. The problem was that a_i_j isn't valid TeX code. a_{ij} is valid, and that's what I assumed you wanted. If you wanted the j lower than the i you would need to use a_{i_j}.
     
  10. Aug 14, 2013 #9
    Oh thanks. It threw me off because I just copied and pasted the code from the "How to type maths equations" thing at the top of the forum. Thanks
     
  11. Aug 14, 2013 #10

    SteamKing

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    IMO = in my opinion
     
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