Transforming matrix to Reduced Row Echelon Form Example [[3,2,4],[2,0,2],[4,2,3]]

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Home > Matrix & Vector calculators > Transforming matrix to Reduced Row Echelon Form example

2. Transforming matrix to Reduced Row Echelon Form example ( Enter your problem )

( Enter your problem )

Example [8-62-67-42-43] $[[8,-6,2],[-6,7,-4],[2,-4,3]]$
Example [324202423] $[[3,2,4],[2,0,2],[4,2,3]]$
Example [111-1-3-3244] $[[1,1,1],[-1,-3,-3],[2,4,4]]$
Example [23410] $[[2,3],[4,10]]$

Other related methods

[8-62-67-42-43] $[[8,-6,2],[-6,7,-4],[2,-4,3]]$
(Previous example)

[111-1-3-3244] $[[1,1,1],[-1,-3,-3],[2,4,4]]$
(Next example)

2. Example [324202423] $[[3,2,4],[2,0,2],[4,2,3]]$

Find Transforming matrix to Reduced Row Echelon Form ...
[324202423] $[[3,2,4],[2,0,2],[4,2,3]]$

Solution:
Reduced row echelon form
Given matrix

	3 $3$	2 $2$	4 $4$
	2 $2$	0 $0$	2 $2$
	4 $4$	2 $2$	3 $3$

R1←R1÷3 $R_1 larr R_1-:3$

=

	1 $1$	23 $2/3$	43 $4/3$
	2 $2$	0 $0$	2 $2$
	4 $4$	2 $2$	3 $3$

R2←R2-2×R1 $R_2 larr R_2-2xx R_1$

=

	1 $1$	23 $2/3$	43 $4/3$
	0 $0$	-43 $-4/3$	-23 $-2/3$
	4 $4$	2 $2$	3 $3$

R3←R3-4×R1 $R_3 larr R_3-4xx R_1$

=

	1 $1$	23 $2/3$	43 $4/3$
	0 $0$	-43 $-4/3$	-23 $-2/3$
	0 $0$	-23 $-2/3$	-73 $-7/3$

R2←R2×(-34) $R_2 larr R_2xx(-3/4)$

=

	1 $1$	23 $2/3$	43 $4/3$
	0 $0$	1 $1$	12 $1/2$
	0 $0$	-23 $-2/3$	-73 $-7/3$

R1←R1-23×R2 $R_1 larr R_1-2/3xx R_2$

=

	1 $1$	0 $0$	1 $1$
	0 $0$	1 $1$	12 $1/2$
	0 $0$	-23 $-2/3$	-73 $-7/3$

R3←R3+23×R2 $R_3 larr R_3+2/3xx R_2$

=

	1 $1$	0 $0$	1 $1$
	0 $0$	1 $1$	12 $1/2$
	0 $0$	0 $0$	-2 $-2$

R3←R3÷(-2) $R_3 larr R_3-:(-2)$

=

	1 $1$	0 $0$	1 $1$
	0 $0$	1 $1$	12 $1/2$
	0 $0$	0 $0$	1 $1$

R1←R1-R3 $R_1 larr R_1- R_3$

=

	1 $1$	0 $0$	0 $0$
	0 $0$	1 $1$	12 $1/2$
	0 $0$	0 $0$	1 $1$

R2←R2-12×R3 $R_2 larr R_2-1/2xx R_3$

=

	1 $1$	0 $0$	0 $0$
	0 $0$	1 $1$	0 $0$
	0 $0$	0 $0$	1 $1$

This material is intended as a summary. Use your textbook for detail explanation.
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[8-62-67-42-43] $[[8,-6,2],[-6,7,-4],[2,-4,3]]$
(Previous example)

[111-1-3-3244] $[[1,1,1],[-1,-3,-3],[2,4,4]]$
(Next example)

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