Question 35276: factor the matrix A into a product of elementary matrices.
A= [1 1]
[2 1]
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! A= [1 1]
[2 1]....
METHOD...WRITE IT IN NORMAL FORM.......1,0
.......................................0,1
STEP.1
USE....R21(-2)...THAT IS NEW ROW 2=OLD ROW 2 + (OLD ROW 1)*(-2)...WE GET
1,1
0,-1
STEP.2
USE R12(1).....THAT IS NEW ROW 1=OLD ROW 1 + OLD ROW 2 *1...WE GET..
1,0
0,-1
STEP.3.
USE C2(-1)....THATIS NEW COLUMN 2 =OLD COLUMN 2*(-1)
1,0
0,1
HENCE WE GOT
I = R12(1)*R21(-2)*A*C2(-1)
HENCE A = {R21(-2)}^(-1)*{R12(1)}^(-1)}*I*{C2(-1)}^(-1)
A = {R21(-2)}^(-1)*{R12(1)}^(-1)}*{C2(-1)}^(-1)
A = {R21(2)}*{R12(-1)}*{C2(-1)}
NOW WE KNOW THAT
I =
1,0
0,1
R21(2) =
1,0
2,1
R12(-1) =
1,-1
0,1
C2(-1) =
1,0
0,-1
HENCE
A = |1,0|*|1,-1|*|1,.0|
..……|2,1|*|0,.1|*|0,-1|
THUS A IS EXPRESSED AS PRODUCT OF ELEMENTARY MATRICES.YOU CAN MULTIPLY AND CHECK
HOPE YOU ARE TAUGHT THE PROCEDURE AND YOU KNOW IT.OTHERWISE PLEASE COME BACK AND WE SHALL EXPLAIN
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