Linear Algebra: Elementary Row Operations

[SNOOTCHIEBOOCHEE]

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

Ers Swaps rows r and s,

Dr([tex] \lambda [/tex]) multiplies row r by [tex] \lambda [/tex]

Trs([tex] \mu [/tex]) adds [tex] \mu [/tex] times row s to row r

compute the determinant of the three matrices you found




I don't 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 doesn't like me so the matrix looks like this

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


PS I am not proficient in latex at all so this might not work

 

[lippyka]

. The determinant of these three matrices is: Ers: The determinant is 1.Dr( \lambda ): The determinant is \lambda .Trs( \mu ): The determinant is 1.