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Ok. A determinants question(Link below).
What I have done?
Well, I tried
Row1 = Row 1+Row 2+row 3 but nothing great.
Can you guys guide me to get the answer??
 one year ago
 one year ago
Ok. A determinants question(Link below). What I have done? Well, I tried Row1 = Row 1+Row 2+row 3 but nothing great. Can you guys guide me to get the answer??
 one year ago
 one year ago

This Question is Closed

shivam_bhallaBest ResponseYou've already chosen the best response.0
http://mypat.in/PaperImages/3/425/Q_4_004.gif
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
can you factor all of the elements
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@UnkleRhaukus ,how exactly??
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
\[\Delta=\left\begin{array}\\1+a^2+a^4&1+ab+a^2b^2&1+ac+a^2c^2\\1+ab+a^2b^2&1+b^2+b^4&1+bc+b^2c^2\\1+ac+a^2c^2&1+bc+b^2c^2&1+c^2+c^4\end{array}\right\]
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
yeah maybe not, i really dont want to do it the normal way
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
Normal way>never :D It would take ages :P
 one year ago

UnkleRhaukusBest ResponseYou've already chosen the best response.0
but it would work in theory, but i would make about ten mistakes
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
I am sure you play around with determinant properties like Row1 = Row 1 + Row 2+Row3 . I mean some tweaking of that sort
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
can we just do it the foolish way?
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@inkyvoyd Sorry, please, In my exam I have only 3 min(max) to solve this question @apoorvk ,let me give it a try and get back to you
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@apoorvk , I did that. But nothing can be taken common out :(
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
I'm going to try this problem
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
Have no fear, for inky is here!
 one year ago

apoorvkBest ResponseYou've already chosen the best response.1
I got common stuff out through C1C2 and C2C3. but, i am still stuck with a trinomial in each ditch..
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
@shivam_bhalla I HAVE AN IDEA
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
aei+bfg+cdhcegbdiafh =a(eifh)+b(fgdj)+c(dgeg)
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
aei+bfg+cdhcegbdiafh aei+bf^2+cbfec^2ah^2
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@inkyvoyd , what is a,b,c,d,e,f,g?? Are you expanding the determinant??
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
I'm wikipediaing, and not making any progress.
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
LOL. @ "wikipediaing" . :)
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
How to wolfram this ??
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@radar sir, any clue ??
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
factor out the commons!!!
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@experimentX , how exactly ?? I mean row wise or column wise. And moreover, what to factor out ??
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
lol ... factoring out would lead to 3 more matrices ..thats ugly... must be some pattern!!
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
Oh. Now get what you meant by factoring .:P I tried that too and observed what you said :)
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
it seems transpose of itself!!
 one year ago

apoorvkBest ResponseYou've already chosen the best response.1
dw:1336584742255:dw this is how far i got then..
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
try making these types to a^4 + a^2 + 1 => a^6  1 (ab)^2 + (ab) + 1 => (ab)^3  1 ... not sure if it can help ... too tired!!!
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
This problem really is trollling me very badly :( I will solve this problem before going to sleeep
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
if you find let met know!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
Oo ...we can drop all ones!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
Oo ... i got zero!! LOL
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
@shivam_bhalla you still there??
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
looks like it got it correct http://www.wolframalpha.com/input/?i=det+{{1%2Ba^2%2Ba^4%2C+1+%2B+%28ab%29+%2B+%28ab%29^2%2C+1+%2B+%28ac%29+%2B+%28ac%29^2}%2C++%09{1+%2B+%28ab%29+%2B+%28ab%29^2%2C+1%2Bb^2%2Bb^4%2C+1+%2B+bc+%2B+%28bc%29^2}%2C++%09{1+%2B+%28ac%29+%2B+%28ac%29^2%2C+1+%2B+bc+%2B+%28bc%29^2%2C+1+%2B+c^2+%2B+c^4}}
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
LOL @experimentX , that is doing it the long way Atleast I know the answer know. :) Thanks for typing out the huge question on wolframalpha :)
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
No .. i know the shortcut too!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
actually i verified answer at wolframalpha!!
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
Ok. Just tell me the method and not the steps because that would literally troll you
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
take out all ones!! sine they will have same values on row .. they will be zero ..
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
Sorry, didn't get you @experimentX
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
dw:1336588777520:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
dw:1336588827490:dw
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
dw:1336588893052:dw
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
i'm not sure how far everyone has got so far but first thoughts: setting a = b we can see that the determinant is zero as R1 = R2 hence (ab) must be a factor
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
whenever matrix has same elements on row or column ... determinant is zero.
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
and by symmetry (bc) and (ac) are
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@experimentX , I never studied that. I only studied that if two rows or 2 colums are proportional to each other, then the determinant of the matrix is zero @eigenschmeigen , Very logical approach which eliminates option (a) for us :)
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
proportional >eg R1 = kR2 so k = 1 is a specific case
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
Oo ... then i must have mistake!!
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
if R1 = R2 then det(M) = 0
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@eigenschmeigen , there is no R1=R2 in @experimentX 's proof
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
Oh my mistake ... i got the answer in fluke
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@experimentX , I wish these flukes come for me too in my exam :P
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
LOL ... i haven't reviewed matrices in long time!! best of luck if you are having exams right now!!
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
LOL. I have college entrance exam's right now :P
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
is this problem solved or still at large? i can have a proper go now i have a pen
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
The problem as of now is unsolved @eigenschmeigen
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
Okay ... i think i got this time!! you can use same technique to reduce matrix!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
dw:1336589808195:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
and then it's simplification!!
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
apply operation as above!!! dw:1336589933207:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
same as you had in your second place!!  minus  one
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
dw:1336590227531:dw
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
dw:1336590458004:dw It can be proved!!
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@experimentX , I will try and let you know in 510 minutes @experimentX
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
okay ... it's just simplification after that. factoring out common factor ... then again you will have 1's and then use same technique ... in the end you will get two linearly dependent columns!! then it will be zero!!
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
i'm just checking my working
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
how do i write matrices on here?
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
@eigenschmeigen , your answer is right. You can use drawing doard :)
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
i like the equation writer, i'm quicker that way: \[\left[\begin{matrix}1+a^2 + a^4 & 1+ ab+a^2b^2 & 1 +ac +a^2c^2 \\ 1 + ab +a^2b^2 & 1+b^2 + b^4 & 1 +ac +a^2c^2 \\ 1 +ac +a^2c^2 & 1 +bc+b^2c^2 & 1 + c^2 + c^4\end{matrix}\right]\]
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
letting a = b we get R1 = R2 letting b = c we get R2 = R3 so the operations to do are R1 R2 = R1' and R2  R3 = R2'
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
\[\left[\begin{matrix}a^4 + a^2  ab  a^2b^2 & a^2b^2 + ab b^2 b^4 & a^2c^2 + ac  bc  b^2c^2 \\ a^2b^2 + ab ac a^2c^2 & b^4 + b^2  bc  b^2c^2 & b^2c^2 + bc c^2  c^4 \\ 1 +ac +a^2c^2 & 1 +bc+b^2c^2 & 1 + c^2 + c^4\end{matrix}\right]\]
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
factor out (ab)(bc)
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
\[(ab)(bc)\left[\begin{matrix}a^3 + a +ba^2 & b^3 + b + ab^2 & c(ac+bc+1) \\ a(ac+ab+1) & b^3 + b +cb^2 & c^3 + c + bc^2 \\ 1 +ac +a^2c^2 & 1 +bc+b^2c^2 & 1 + c^2 + c^4\end{matrix}\right]\]
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
letting a = b we now have C1 = C2 so we can see that (ab) is again a factor. this narrows it down to B as we will have (ab)^2 in our answer
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
you can continue to factorise if you want, but this is sufficient to get the right option.
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
its not said in many textbooks but i find using factor theorem is really useful for factorising determinants, as it tells us an operation that will result in something we can factor
 one year ago

shivam_bhallaBest ResponseYou've already chosen the best response.0
Thank you @eigenschmeigen and @experimentX for both of your solutions :D Thanks for taking your time :)
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
no problem, love matrices :)
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
looks like i didn't get that right ... i'm embarrassed. looks like 'linear algebra' is the first thing i should do after i'm done with calc
 one year ago

eigenschmeigenBest ResponseYou've already chosen the best response.1
what else does linear algebra cover?
 one year ago

experimentXBest ResponseYou've already chosen the best response.2
well ... all forgot!! let's see ... i have a book here. Linear algebra  Serge Lang Vectors, Vector spaces, Matirces, Linear mappings, Linear mappings and matrices, .... Groups, Rings, Convex Sets ... Appendix I thought \( \Delta\) on wolfram was the answer!!
 one year ago
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