Imtiaz7
  • Imtiaz7
Help Please...!!!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Imtiaz7
  • Imtiaz7
Convert following matrix into Reduced Echlon Form:
Imtiaz7
  • Imtiaz7
|dw:1438863140426:dw|
UsukiDoll
  • UsukiDoll
just reduce echelon form right?

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UsukiDoll
  • UsukiDoll
so what we need is an upper triangular matrix which means that below the main diagonal we need all 0's we can achieve this by using row operations by swapping rows, multiplying a row by a scalar number, or add/subtract rows and replace the old row with the new result after that computation
UsukiDoll
  • UsukiDoll
keep in mind that we need a 1 always at the top left the 1 also has to go towards the right and the bottom... we also need a row of zeros
Imtiaz7
  • Imtiaz7
wait I've solve this, can you please tell me is this right?
UsukiDoll
  • UsukiDoll
|dw:1438863440670:dw| so the places I've circled is the main diagonal so we need to get rid of the 3 , -1, and 4 using row operations... yeah sure.
UsukiDoll
  • UsukiDoll
anyway... -3r1 + r2 -> r2 r1+ r3 - > r3
UsukiDoll
  • UsukiDoll
|dw:1438863691395:dw||dw:1438863716259:dw|
UsukiDoll
  • UsukiDoll
|dw:1438863747952:dw|
UsukiDoll
  • UsukiDoll
hmmm gonna make life a bit easier by 1/2r3->r3
UsukiDoll
  • UsukiDoll
|dw:1438863802231:dw|
UsukiDoll
  • UsukiDoll
-r2+11r3 ->r3
UsukiDoll
  • UsukiDoll
|dw:1438863836507:dw|
UsukiDoll
  • UsukiDoll
1/10 r3 - >r3 1/11 r2 - > r2
UsukiDoll
  • UsukiDoll
|dw:1438863882447:dw|
UsukiDoll
  • UsukiDoll
do you have a matrix that looks like this? ^
Imtiaz7
  • Imtiaz7
UsukiDoll
  • UsukiDoll
how did you get 20/11 ?
Imtiaz7
  • Imtiaz7
by multiplying Row 2 by -2 and add it in row 3(-2*1/11 + 2)
UsukiDoll
  • UsukiDoll
hmmm dealing with fractions that early is killer though
UsukiDoll
  • UsukiDoll
because what I've done to the third row was divide by 1/2 all over row 3 so I would have just 0 1 1
UsukiDoll
  • UsukiDoll
so when I had 0 11 1 0 1 1 I distributed the negative sign on row 2 and then multiply row 3 with 11 -r2+11r^3 -> r^3
Imtiaz7
  • Imtiaz7
Uhm so i i did wrong?
UsukiDoll
  • UsukiDoll
0 -11 -1 0 11 11 adding them together would make it 0 0 10 and then 1/10r3 ->r3 to get rid of that 10 to have 0 0 1
Imtiaz7
  • Imtiaz7
but in last it becomes in reduced echlon form; isnt?
UsukiDoll
  • UsukiDoll
and then to have the 1 in the middle I had to divide the whole second row by 1/11
UsukiDoll
  • UsukiDoll
somehow our first rows are different but the second and third is the same..
Imtiaz7
  • Imtiaz7
does my answer is correct?
UsukiDoll
  • UsukiDoll
it should be as long as it followed the reduce echelon rules.. and it does. we do have an upper triangular matrix and our 1 is going down and shifted to the right
Imtiaz7
  • Imtiaz7
Yes! So our answers are different, but rules are same!
UsukiDoll
  • UsukiDoll
hmm I'm assuming that an extra step was taken to get rid of the -2 on the first row. unless we are required to get RREF form, that's not required. What's required is the numbers until the main diagonal go to 0.
UsukiDoll
  • UsukiDoll
check this one out... it also did something different but ended up with the same thing before taking RREF form oh that 1 in the third row got blocked out, but noticed how this calculator did something I disagree with, but still ends up following the rules?
Imtiaz7
  • Imtiaz7
wait let me check it
UsukiDoll
  • UsukiDoll
that was done by a calculator bot... I really hated that 0 0 54/11 but by multiplying 11/54r3 -> r3 0 0 1
Imtiaz7
  • Imtiaz7
@UsukiDoll the question is different there, that is there is 1 instead of 1 in first row
Imtiaz7
  • Imtiaz7
-1*
UsukiDoll
  • UsukiDoll
ugh a typo.. yeah this is way late at night... on my end.
UsukiDoll
  • UsukiDoll
one sec.
UsukiDoll
  • UsukiDoll
still has that big fraction 20/11 on row 3 but 11/20r3 - >r3 makes it 0 0 1
Imtiaz7
  • Imtiaz7
my answer is correct!!!
UsukiDoll
  • UsukiDoll
mhm
Imtiaz7
  • Imtiaz7
:) lol Thank you so much @UsukiDoll to help me..
UsukiDoll
  • UsukiDoll
XD you're welcome... these questions always come up very late at night, so typos are bound to happen... typed too fast XD
Imtiaz7
  • Imtiaz7
Its okay, when i post i dont run xD
UsukiDoll
  • UsukiDoll
yay I got it right too XD |dw:1438865533703:dw| row operation #5 on the correct image has the same matrix I had... only in fewer steps.
UsukiDoll
  • UsukiDoll
but as long as the rules aren't broken for row echelon form, then everything will be fine ^_^
Imtiaz7
  • Imtiaz7
Yup @UsukiDoll rules are for obey uhm i think so lol
Imtiaz7
  • Imtiaz7
@UsukiDoll ?
UsukiDoll
  • UsukiDoll
hmmm?
Imtiaz7
  • Imtiaz7
There is still a confusion uhm the answer you showed me are correct one but in my answer in fist row there is -9/11, still is it right?
UsukiDoll
  • UsukiDoll
you mean for this right http://assets.openstudy.com/updates/attachments/55c34eede4b06d80932e63a6-imtiaz7-1438864107356-20150806_172006.jpg ?
UsukiDoll
  • UsukiDoll
as long as you have an upper triangular matrix which means all 0's below the main diagonal and have a 1 on the top left that goes to the bottom and right... I don't see a problem.
Imtiaz7
  • Imtiaz7
Okay :)
Imtiaz7
  • Imtiaz7
Once again thanks a lot :)
UsukiDoll
  • UsukiDoll
we could RREF that last matrix with that -9/11 if you want
UsukiDoll
  • UsukiDoll
to show that we can get an identity matrix out of some more row operations..
UsukiDoll
  • UsukiDoll
|dw:1438866425233:dw| this was the matrix you had in REF form right?
Imtiaz7
  • Imtiaz7
Yes
UsukiDoll
  • UsukiDoll
I would use row 3 to get rid of the remaining numbers above the main diagonal, but I hate dealing with fractions so 11r2 - >r2 11r1 -> r1
UsukiDoll
  • UsukiDoll
|dw:1438866522476:dw|
UsukiDoll
  • UsukiDoll
-r3+r2 - > r2 -9r3 + r1 - > r1
UsukiDoll
  • UsukiDoll
|dw:1438866568376:dw||dw:1438866589363:dw|
Imtiaz7
  • Imtiaz7
@UsukiDoll can i give you another medal bc your math is too good
UsukiDoll
  • UsukiDoll
1/11r2 - >r2 1/11 r1 -> r1... I wish we can give more than 1 medal XD
UsukiDoll
  • UsukiDoll
|dw:1438866634762:dw| a-ha identity matrix! so we got RREF XD
Imtiaz7
  • Imtiaz7
lol
UsukiDoll
  • UsukiDoll
which means your row operations from earlier were correct... otherwise we wouldn't get RREF
Imtiaz7
  • Imtiaz7
yes...

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