waleed_imtiaz
  • waleed_imtiaz
Hey everybody... Please explain my question ...
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
terenzreignz
  • terenzreignz
It's now or never :P
waleed_imtiaz
  • waleed_imtiaz
heehehe wait just my pics are uploading... :)
waleed_imtiaz
  • waleed_imtiaz

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terenzreignz
  • terenzreignz
Doesn't this belong in Physics? D:
waleed_imtiaz
  • waleed_imtiaz
this is the question of circuit analysis by david irwin...I want u guys to tell me how to solve these equations by matrices...!
terenzreignz
  • terenzreignz
ohh.. must have spoken too soon D:
waleed_imtiaz
  • waleed_imtiaz
no dear... read my complete question...and plz help me out...these two pages is the complete question... This is the question of mathematics... how to solve 4 or 5 equations by matrices?
waleed_imtiaz
  • waleed_imtiaz
u understand my question @terenzreignz ?
terenzreignz
  • terenzreignz
It's bad enough I don't know this Physics stuff, but matrices aren't my thing... let's have some more eyes on it ^_^ @ganeshie8
terenzreignz
  • terenzreignz
Although, when it comes to systems, there might be something I can scrape up...
waleed_imtiaz
  • waleed_imtiaz
okey let it be then...! I want u guyz to explain me the method of solving 4 equations by matrices... not by simultaneously solving them...
waleed_imtiaz
  • waleed_imtiaz
I hope ur reply might not get too late :)
terenzreignz
  • terenzreignz
Okay, let's see... \[\Large \left.\begin{matrix}159v_2-43v_3-12.6v_4+12.6v_5=756\\v_2-2v_4-v_5=-24\\-v_2+v_3-12v_4+12v_5=45\\5v_4-4v_5=12\end{matrix}\right.\]
terenzreignz
  • terenzreignz
Everything correct?
terenzreignz
  • terenzreignz
@waleed_imtiaz
waleed_imtiaz
  • waleed_imtiaz
here in the first equation.... its not 12.6 ...its 126... everything else is correct/..
terenzreignz
  • terenzreignz
\[\Large \left.\begin{matrix}159v_2-43v_3-126v_4+126v_5=756\\v_2-2v_4-v_5=-24\\-v_2+v_3-12v_4+12v_5=45\\5v_4-4v_5=12\end{matrix}\right.\]
waleed_imtiaz
  • waleed_imtiaz
okey thats fine... now how to solve by matrices...?
terenzreignz
  • terenzreignz
Okay then, first, make a matrix containing all the coefficients, in proper order, for v2, v3, v4, and v5. \[\Large \left[\begin{matrix}159&-43&-126&126\\1&0&-2&-1\\-1&1&-12&12\\0&0&5&-4\end{matrix}\right]\]
waleed_imtiaz
  • waleed_imtiaz
okey got it... then next ???
terenzreignz
  • terenzreignz
It's multiplied to this column matrix: \[\Large \left[\begin{matrix}159&-43&-126&126\\1&0&-2&-1\\-1&1&-12&12\\0&0&5&-4\end{matrix}\right]\left[\begin{matrix}v_2\\v_3\\v_4\\v_5\end{matrix}\right]\]
waleed_imtiaz
  • waleed_imtiaz
got it... I knoww... and it will equals the matrix of all hte coefficients in the equation after the equal sign.... then next?
terenzreignz
  • terenzreignz
\[\Large \left[\begin{matrix}159&-43&-126&126\\1&0&-2&-1\\-1&1&-12&12\\0&0&5&-4\end{matrix}\right]\left[\begin{matrix}v_2\\v_3\\v_4\\v_5\end{matrix}\right]=\left[\begin{matrix}756\\-24\\45\\12\end{matrix}\right]\] yeah...
terenzreignz
  • terenzreignz
Did your instructor do an example problem? How did your instructor do it, with row-operations?
waleed_imtiaz
  • waleed_imtiaz
thats okey.... thne?
terenzreignz
  • terenzreignz
Kramer's rule? or perhaps inverses?
terenzreignz
  • terenzreignz
I need help :( @hartnn ?
waleed_imtiaz
  • waleed_imtiaz
I dont know how to solve it and my professor also didn't tell me because the time was short.... so I consider it a few methods of solving it...I think it can be done by row or column operations? or by crammer rule... or if i go with inverses,,, it will be a big question .... its bit of a mess.... taking inverse of 4 by 4 matrix... is a big task... so i think we should go with the method that uses less mathematical calculations...
waleed_imtiaz
  • waleed_imtiaz
yea i need help too :( @hartnn @amistre64
ganeshie8
  • ganeshie8
reduce it to triangular form and back substitute
waleed_imtiaz
  • waleed_imtiaz
can u solve it for me? :(
waleed_imtiaz
  • waleed_imtiaz
i want complete solution because i tried it but failed... reducing it to upper or lower triangular matrix ...is a mess....
ganeshie8
  • ganeshie8
i dont see why its a mess yet, let me try :)
ganeshie8
  • ganeshie8
yep ! wolfram is giving all fractions, so manually solving using matrices is pain http://www.wolframalpha.com/input/?i=solve++%7B%7B159%2C-53%2C-126%2C126%7D+%2C+%7B1%2C0%2C-2%2C-1%7D%2C+%7B-1%2C1%2C-12%2C12%7D%2C+%7B0%2C0%2C5%2C-4%7D%7D%7B%7Bw%7D%2C%7Bx%7D%2C%7By%7D%2C%7Bz%7D%7D+%3D+%7B%7B756%7D%2C+%7B-24+%7D%2C+%7B45%7D%2C+%7B12%7D%7D
waleed_imtiaz
  • waleed_imtiaz
yes...! just show me how u can solve it...? by taking inverses or by crammers rule or by row or column operations... @ganeshie8
ganeshie8
  • ganeshie8
okay ! lets do elimination
ganeshie8
  • ganeshie8
first exchange R1 & R2, i hope you're familiar wid row operations a bit ?
waleed_imtiaz
  • waleed_imtiaz
but u can tell me :) because its long time when i studied these matrices... thats why I am confused... may be i guess that when we interchange the rows or columns we take negative sign outside? right?
ganeshie8
  • ganeshie8
thats for determinants, but when doing row operations, we can interchange rows freely (think of each row as an equaiton) order of equations doesnt matter
waleed_imtiaz
  • waleed_imtiaz
okey then interchanging rows 1 and 2... then?
waleed_imtiaz
  • waleed_imtiaz
can we reduce it to upper or lower triangular matrix? my frnd told me to do so...and then solve the augmented matrix...
ganeshie8
  • ganeshie8
augmented matrix :- 159 -43 -126 126 756 1 0 -2 -1 -24 -1 1 -12 12 45 0 0 5 -4 12
ganeshie8
  • ganeshie8
our goal is to change it to upper triangular matrix
waleed_imtiaz
  • waleed_imtiaz
yes okey.... then how we'll change it to upper triangular matrix?
ganeshie8
  • ganeshie8
exchange R1 & R2 1 0 -2 -1 -24 159 -43 -126 126 756 -1 1 -12 12 45 0 0 5 -4 12
ganeshie8
  • ganeshie8
next do, R2 - 159R1
ganeshie8
  • ganeshie8
and, R3+R1
waleed_imtiaz
  • waleed_imtiaz
Are u going to make the first column asn this? 1 0 0 0
waleed_imtiaz
  • waleed_imtiaz
@ganeshie8
ganeshie8
  • ganeshie8
Yes, 1 0 -2 -1 -24 0 -43 192 -33 4572 0 1 -14 11 21 0 0 5 -4 12
ganeshie8
  • ganeshie8
you pls verify my calculations also ok :)
ganeshie8
  • ganeshie8
Next, exchange R2 & R3
ganeshie8
  • ganeshie8
1 0 -2 -1 -24 0 1 -14 11 21 0 -43 192 -33 4572 0 0 5 -4 12
ganeshie8
  • ganeshie8
R3 + 43R2
waleed_imtiaz
  • waleed_imtiaz
wait wait wait...how u wrote -33 on the second row wihile doing R2-159R1?
waleed_imtiaz
  • waleed_imtiaz
waiting for ur reply...!!!
ganeshie8
  • ganeshie8
yes thats a mistake, just checking if you're alert or not ;) 1 0 -2 -1 -24 0 -43 192 285 4572 0 1 -14 11 21 0 0 5 -4 12
waleed_imtiaz
  • waleed_imtiaz
oh hoo :p thats good :)
ganeshie8
  • ganeshie8
does that look correct right after doing, R2-159R1
waleed_imtiaz
  • waleed_imtiaz
yes...
ganeshie8
  • ganeshie8
ok lets keep going
ganeshie8
  • ganeshie8
Next, exhange R2 & R3
ganeshie8
  • ganeshie8
1 0 -2 -1 -24 0 1 -14 11 21 0 -43 192 285 4572 0 0 5 -4 12
ganeshie8
  • ganeshie8
R3+43R1
ganeshie8
  • ganeshie8
1 0 -2 -1 -24 0 1 -14 11 21 0 0 -410 758 5475 0 0 5 -4 12
ganeshie8
  • ganeshie8
exchange R3 & R4
ganeshie8
  • ganeshie8
1 0 -2 -1 -24 0 1 -14 11 21 0 0 5 -4 12 0 0 -410 758 5475
ganeshie8
  • ganeshie8
R3/5
ganeshie8
  • ganeshie8
1 0 -2 -1 -24 0 1 -14 11 21 0 0 1 -4/5 12/5 0 0 -410 758 5475
waleed_imtiaz
  • waleed_imtiaz
i have to go to MASJID...can we talk about this at nite? or u give me the solution and i will see it when I will come online...okey :) I am understanding ur calculations...
ganeshie8
  • ganeshie8
R4+410R3
ganeshie8
  • ganeshie8
ok np :) u go, il complete
waleed_imtiaz
  • waleed_imtiaz
okey I will see after I come back... :) thanks @ganeshie8
ganeshie8
  • ganeshie8
1 0 -2 -1 -24 0 1 -14 11 21 0 0 1 -4/5 12/5 0 0 0 430 6459
ganeshie8
  • ganeshie8
R4/430
ganeshie8
  • ganeshie8
1 0 -2 -1 -24 0 1 -14 11 21 0 0 1 -4/5 12/5 0 0 0 1 15.02
ganeshie8
  • ganeshie8
Now the coefficient matrix is upper triangular. We're done
ganeshie8
  • ganeshie8
\(\large v_5 = 15.02\) \(\large v_4 - \frac{4}{5}v_5 = 12/5\) \(\large v_3 - 14 v_4 +11 v_5 = 21\) \(\large v_2 - 2 v_4 - v_5 = -24\)
ganeshie8
  • ganeshie8
simply substitute values, verify the solution wid wolfram http://www.wolframalpha.com/input/?i=solve++%7B%7B159%2C-43%2C-126%2C126%7D+%2C+%7B1%2C0%2C-2%2C-1%7D%2C+%7B-1%2C1%2C-12%2C12%7D%2C+%7B0%2C0%2C5%2C-4%7D%7D%7B%7Bw%7D%2C%7Bx%7D%2C%7By%7D%2C%7Bz%7D%7D+%3D+%7B%7B756%7D%2C+%7B-24+%7D%2C+%7B45%7D%2C+%7B12%7D%7D
waleed_imtiaz
  • waleed_imtiaz
thanks alott... I got it...! iits lengthy but its the solution :) I will practice more questions like this to make it a good understanding :) thanks @ganeshie8
ganeshie8
  • ganeshie8
cool :)
waleed_imtiaz
  • waleed_imtiaz
and what about inverses and about crammer rule? I know now I am teasing u ... but if u have time can u please solve this question by crammer's rule and by inverses... just do it not here because i think its difficult to write here... do it on some register and then send me the pic if u are free?
ganeshie8
  • ganeshie8
crammars ruleinvolves finding 5 determinants, for a 4x4 matrix
ganeshie8
  • ganeshie8
inverse method, we need to find the inverse one time. we can use Gause Jordan method for finding inverse which is very simple
waleed_imtiaz
  • waleed_imtiaz
I dont know whats that method.... okey let me not disturb u and I will search gause jordan method and also will search for crammers rule for 4 by 4 or 5 by 5 matrices... just give me the link if easy... :)
waleed_imtiaz
  • waleed_imtiaz
If I will be unable to understand the method then I will ask u...okey :)
ganeshie8
  • ganeshie8
crammars rule is easy to understand, but for Gauss Jordan method - we need to do the same row operations we did before
ganeshie8
  • ganeshie8
yea sure, just ping me when u may get stuck.. :)
waleed_imtiaz
  • waleed_imtiaz
okey I will .... thanks a lot... thats the best response I have got since I joined this site...
ganeshie8
  • ganeshie8
thanks too :)

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