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2 Questions concerning determinants

  1. Nov 16, 2009 #1
    1. The problem statement, all variables and given/known data

    First Question. How many even Permutations does a 5x5 matrix have? In other words how many permutations are there that would make it +1 instead of -1.

    Second Question. v= (3,2) w= (4,1) use determinants to find the area of a triangle with sides v, w and v+w

    2. Relevant equations



    3. The attempt at a solution

    First Question. I know you can write them all out, but is there some kind of formula to find how many permutations there are and determine whether the are even or odd? I assume it has something to do with factorials

    Second question. I don't know what to do with the matrix when it is not a square, so how do you find a determinant of a triangle? I could use 1/2bh but the problem asks to use determinants specifically
     
  2. jcsd
  3. Nov 16, 2009 #2

    lanedance

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    first - how many choices is there for the first row? then say you have chosen first row, how many for the 2nd... and so on

    2nd - do you know about vector cross products? the length of a vector cross product is the area of the parallelogram made by the 2 vectors... relate this to the determinant equation
     
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