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Homework Help: Determinant n

  1. Oct 29, 2011 #1
    1. The problem statement, all variables and given/known data
    I have to find a determinant for
    1 2 3 ... n
    -1 0 3 ... n
    -1 -2 0 ... n
    -1 -2 -3 ... 0
    but I have very little clue how to proceed, because the mathematics material that I was given is very vague about this. Any help would be greatly appreciated.

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Oct 29, 2011 #2
    Does -1 -2 -3 ... 0 represent the final row of the matrix meaning the the lowest right member is 0?
  4. Oct 29, 2011 #3

    I like Serena

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    Homework Helper

    Welcome to PF, Helloes! :smile:

    The main rule about calculating determinants, is that you can add a multiple of a row to another row, without changing the determinant.
    Same thing for columns: you can add (or subtract) a multiple of one column to another column.

    Now let's try a couple of determinants.

    What is |1|?

    What is [itex]\begin{vmatrix}1&2\\-1&0\end{vmatrix}[/itex]?

    What is [itex]\begin{vmatrix}1&2&3\\-1&0&3\\-1&-2&0\end{vmatrix}[/itex]?

    What is [itex]\begin{vmatrix}1&2&3&4\\-1&0&3&4\\-1&-2&0&4\\-1&-2&-3&0\end{vmatrix}[/itex]?
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