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Can both of this vector combine become the following matrix?

  1. Feb 21, 2009 #1
    vector A : ai+bj
    vector B : ci+dj

    can both of this vector combine become the following matrix?

    [tex]\stackrel{a}{c}[/tex] [tex]\stackrel{b}{d}[/tex] or [tex]\stackrel{a}{b}[/tex] [tex]\stackrel{c}{d}[/tex]


    hope anyone can tell me more about this..coz i search a lot a wiki there..~~
     
  2. jcsd
  3. Feb 21, 2009 #2
    Re: matrix

    What do you mean by combine?
     
  4. Feb 21, 2009 #3
    Re: matrix

    do you mean put vectors together in column or in row?
     
  5. Feb 21, 2009 #4

    Hootenanny

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    Staff Emeritus
    Science Advisor
    Gold Member

    Re: matrix

    You just need to consider the definition of matrix multiplication. You want to find a matrix A such that

    [tex]\left(\begin{array}{c}
    a\bold{i} + b\bold{j} \\
    c\bold{i} + d\bold{j}
    \end{array}\right) = A \left(\begin{array}{c}
    \bold{i} \\
    \bold{j}
    \end{array}\right) =
    \left(\begin{array}{cc}
    a_{11} & a_{12} \\
    a_{21} & a_{22}
    \end{array}\right)
    \left(\begin{array}{c}
    \bold{i} \\
    \bold{j}
    \end{array}\right)[/tex]

    From this you should be able to work out the required components.
     
  6. Feb 21, 2009 #5

    HallsofIvy

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    Re: matrix

    You can put numbers together any way you please and make a matrix. The question is how do you want that matrix to be related to the original vectors and what do you want to do with it?
     
  7. Feb 23, 2009 #6
    Re: matrix

    I think i found the answer by the definition of the mutiplication of matrix...
    Thx a lot..~
    coz when i read about the article of the transformation matrix i can't get it..hehe thx
     
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