Hey everybody... Please explain my question ...

- waleed_imtiaz

Hey everybody... Please explain my question ...

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- schrodinger

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- terenzreignz

It's now or never :P

- waleed_imtiaz

heehehe wait just my pics are uploading... :)

- waleed_imtiaz

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## More answers

- terenzreignz

Doesn't this belong in Physics? D:

- 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...!

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- terenzreignz

ohh.. must have spoken too soon D:

- 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

u understand my question @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

Although, when it comes to systems, there might be something I can scrape up...

- 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

I hope ur reply might not get too late :)

- 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

Everything correct?

- terenzreignz

@waleed_imtiaz

- waleed_imtiaz

here in the first equation.... its not 12.6 ...its 126... everything else is correct/..

- 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

okey thats fine... now how to solve by matrices...?

- 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

okey got it... then next ???

- 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

got it... I knoww... and it will equals the matrix of all hte coefficients in the equation after the equal sign.... then next?

- 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

Did your instructor do an example problem? How did your instructor do it, with row-operations?

- waleed_imtiaz

thats okey.... thne?

- terenzreignz

Kramer's rule? or perhaps inverses?

- terenzreignz

I need help :(
@hartnn ?

- 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

yea i need help too :( @hartnn @amistre64

- ganeshie8

reduce it to triangular form and back substitute

- waleed_imtiaz

can u solve it for me? :(

- waleed_imtiaz

i want complete solution because i tried it but failed... reducing it to upper or lower triangular matrix ...is a mess....

- ganeshie8

i dont see why its a mess yet, let me try :)

- 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

yes...! just show me how u can solve it...? by taking inverses or by crammers rule or by row or column operations... @ganeshie8

- ganeshie8

okay ! lets do elimination

- ganeshie8

first exchange R1 & R2, i hope you're familiar wid row operations a bit ?

- 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

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

okey then interchanging rows 1 and 2... then?

- 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

augmented matrix :-
159 -43 -126 126 756
1 0 -2 -1 -24
-1 1 -12 12 45
0 0 5 -4 12

- ganeshie8

our goal is to change it to upper triangular matrix

- waleed_imtiaz

yes okey.... then how we'll change it to upper triangular matrix?

- 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

next do, R2 - 159R1

- ganeshie8

and, R3+R1

- waleed_imtiaz

Are u going to make the first column asn this?
1
0
0
0

- waleed_imtiaz

@ganeshie8

- ganeshie8

Yes,
1 0 -2 -1 -24
0 -43 192 -33 4572
0 1 -14 11 21
0 0 5 -4 12

- ganeshie8

you pls verify my calculations also ok :)

- ganeshie8

Next, exchange R2 & R3

- ganeshie8

1 0 -2 -1 -24
0 1 -14 11 21
0 -43 192 -33 4572
0 0 5 -4 12

- ganeshie8

R3 + 43R2

- waleed_imtiaz

wait wait wait...how u wrote -33 on the second row wihile doing R2-159R1?

- waleed_imtiaz

waiting for ur reply...!!!

- 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

oh hoo :p thats good :)

- ganeshie8

does that look correct right after doing, R2-159R1

- waleed_imtiaz

yes...

- ganeshie8

ok lets keep going

- ganeshie8

Next, exhange R2 & R3

- ganeshie8

1 0 -2 -1 -24
0 1 -14 11 21
0 -43 192 285 4572
0 0 5 -4 12

- ganeshie8

R3+43R1

- ganeshie8

1 0 -2 -1 -24
0 1 -14 11 21
0 0 -410 758 5475
0 0 5 -4 12

- ganeshie8

exchange R3 & R4

- ganeshie8

1 0 -2 -1 -24
0 1 -14 11 21
0 0 5 -4 12
0 0 -410 758 5475

- ganeshie8

R3/5

- 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

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

R4+410R3

- ganeshie8

ok np :) u go, il complete

- waleed_imtiaz

okey I will see after I come back... :) thanks @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

R4/430

- 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

Now the coefficient matrix is upper triangular. We're done

- 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

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

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

cool :)

- 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

crammars ruleinvolves finding 5 determinants, for a 4x4 matrix

- 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

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

If I will be unable to understand the method then I will ask u...okey :)

- ganeshie8

crammars rule is easy to understand,
but for Gauss Jordan method - we need to do the same row operations we did before

- ganeshie8

yea sure, just ping me when u may get stuck.. :)

- waleed_imtiaz

okey I will .... thanks a lot... thats the best response I have got since I joined this site...

- ganeshie8

thanks too :)

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