2 Questions concerning determinants

[jvent051]

Homework Statement

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

Homework Equations

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

 

[lanedance]

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