Elementary Row Matricies
alexwang0518
How do you figure out what 'elementary matrix' to multiply by when computing the determinant? Weisbart did an example where he found the determinant by E1E2E3E4...=I (where En is an elementary row matrix) but he didn't explain how he got the elementary row matrices, he kind of just wrote them. Help appreciated!
ericpan64: June 5, 2015, 12:12 p.m.
I believe that En (elementary row matrix) is a matrix representing the nth step when you're row reducing So, for ex., E1 is a matrix that represents the first step in row-reducing (that is, if you multiply E1*A, that performs the first step in your row-reducing) So if while row-reducing, if for your first step you want to swap rows 2 and 3, E1 would be $(1,0,0) # (0, 0, 1) (0, 1,0)$ because multiplying E1 * A would give you A with the rows 2 and 3 swapped. The hashtag is there because idk how to format a matrix on this site Hope that helped!
ericpan64: June 5, 2015, 12:13 p.m.
A better way to phrase it is En is a matrix representing an 'elementary' operation