# Linear Algebra: Elementary Row Operations

1. Apr 22, 2007

### SNOOTCHIEBOOCHEE

Elementary Matrices: Let A be a mxn matrix. Write down mxm matrices Ers, Dr($$\lambda$$) and Trs($$\mu$$)

Ers Swaps rows r and s,

Dr($$\lambda$$) multiplies row r by $$\lambda$$

Trs($$\mu$$) adds $$\mu$$ times row s to row r

compute the determinant of the three matrices you found

I dont have trouble with the determinant part of this problem. i am however stuck finding Ers and Trs. i also am not sure if my soltion for Dr (lambda) is correct. i got the following (assuming row r is the top row and mxm=3x3)

Ok latex doesnt like me so the matrix looks like this

[ Lambda , 0 , 0
0 1 0
0 0 1]

PS im not proficient in latex at all so this might not work

Last edited: Apr 22, 2007