[Math] Reduced Row Echelon Form

H

Haunt

Veteran XX
Math gurus, teach me. Please :sunny:


Here's my matrix
Code: 
1   1  -1   1
1  -1   7   8 
-1  1  -5  -5

In reducing this biatch down, I got 0 -2 8 7 in row 2 and 0 2 -6 -4 in the third. I swapped R3 with R2 (so that I could multiply the new R2 with 1/2 and get 0 1 -3 -2)

Apparently, that's where I went wrong. Can you only use row swapping as a technique to get the rightmost nonzero column up to the first row?

..I assumed that row swapping wasn't a big deal since you can swap equations around in a system without affecting the system. (or at least, I don't think it affects the system)

I came out with an answer of
Code: 
1   0   0  -1
0   1   0   1
0   0   1  -1

but the answer, according to Linear Algebra Toolkit
is
Code: 
 1  	 0  	 0  	 0 
 0  	 1  	 0  	 5/2 
 0  	 0  	 1  	 3/2

wtf, tw?
 
Code: 
1   1  -1   1
1  -1   7   8 
-1  1  -5  -5

add row 3 to row 2 and row 3 to row 1

Code: 
0   2  -6   -4
0  0   2   3 
-1  1  -5  -5

shift all rows down 1

Code: 
-1  1  -5  -5
0   2  -6   -4
0  0   2   3

divide rows 2 and 3 by 2, multiply row 1 by -1

Code: 
1  -1  5  5
0   1  -3   -2
0  0   1   1.5

add 3*r3 to r2, subtract 5*r3 from r1

Code: 
1  -1  0  -2.5
0   1  0   2.5
0  0   1   1.5

add row 2 to row 1

Code: 
1  0  0  0
0   1  0   2.5
0  0   1   1.5

row swapping can be done you are just shitty at algebra probably

column swapping can also be done as long as you remember to switch the corresponding variables but thats really just a time saver for hand computations
 
Last edited:
Artemis Pockels said:
Code: 
1   1  -1   1
1  -1   7   8 
-1  1  -5  -5

add row 3 to row 2 and row 3 to row 1

Code: 
0   2  -6   -4
0  0   2   3 
-1  1  -5  -5

shift all rows down 1

Code: 
-1  1  -5  -5
0   2  -6   -4
0  0   2   3

divide rows 2 and 3 by 2, multiply row 1 by -1

Code: 
1  -1  5  5
0   1  -3   -2
0  0   1   1.5

add 3*r3 to r2, subtract 5*r3 from r1

Code: 
1  -1  0  -2.5
0   1  0   2.5
0  0   1   1.5

add row 2 to row 1

Code: 
1  0  0  0
0   1  0   2.5
0  0   1   1.5

row swapping can be done you are just shitty at algebra probably

column swapping can also be done as long as you remember to switch the corresponding variables but thats really just a time saver for hand computations
Click to expand...

you are a fucking bro man

i cant believe you went through all that arithmetic for this dumb turd

respect
 
yeah, you messed up your calculation somewhere. I had forgotten how to do this and just dug up the algorithm in my book. Took me two attempts to get the right answer. I hated this part of linear algebra. I'm much happier knowing a rref exists and be done with it.
 
osse697 said:
you are a fucking bro man

i cant believe you went through all that arithmetic for this dumb turd

respect
Click to expand...

the only way you can really screw it up is if you do the arithmetic wrong so the only way to show somebody how to do it is to go step by step

and this matrix happened to be pretty easy with regard to the numbers in it and its size (any 3x3 matrix can be reduced in 6 steps or less always: divide row 1 by the its first element to get 1, zero out the first elements of the other 2 rows, divide row 2 by its second element to get 1, zero out the second elements of the other two rows, divide row 3 by its third element to get one, zero out other two rows => read off answers)
 
rref is probably the easiest part of linear algebra.
Calculator and matlab aren't going to help you on an exam.
 
Faze said:
yeah, you messed up your calculation somewhere. I had forgotten how to do this and just dug up the algorithm in my book. Took me two attempts to get the right answer. I hated this part of linear algebra. I'm much happier knowing a rref exists and be done with it.
Click to expand...

:lol:
 
you might find my condensed lin alg notes from a while back useful

Linear.algebra.complete

i spammed half of my class and and sold a shitload of copies for 10 bucks a piece back in the day

although it doesn't go to through a lot of stuff like vector spaces and subspaces, bases, gauss-jordan, etc. because that was part of a previous course.
 
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