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shivam_bhalla
Group Title
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??
 2 years ago
 2 years ago
shivam_bhalla Group Title
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??
 2 years ago
 2 years ago

This Question is Closed

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
http://mypat.in/PaperImages/3/425/Q_4_004.gif
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
can you factor all of the elements
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@UnkleRhaukus ,how exactly??
 2 years ago

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

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
yeah maybe not, i really dont want to do it the normal way
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
Normal way>never :D It would take ages :P
 2 years ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.0
but it would work in theory, but i would make about ten mistakes
 2 years ago

shivam_bhalla Group TitleBest 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
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@apoorvk
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
can we just do it the foolish way?
 2 years ago

apoorvk Group TitleBest ResponseYou've already chosen the best response.1
Hmm, tried C1  C2?
 2 years ago

shivam_bhalla Group TitleBest 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
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@apoorvk , I did that. But nothing can be taken common out :(
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
I'm going to try this problem
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
Have no fear, for inky is here!
 2 years ago

apoorvk Group TitleBest 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..
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
@shivam_bhalla I HAVE AN IDEA
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
aei+bfg+cdhcegbdiafh =a(eifh)+b(fgdj)+c(dgeg)
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
aei+bfg+cdhcegbdiafh aei+bf^2+cbfec^2ah^2
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@inkyvoyd , what is a,b,c,d,e,f,g?? Are you expanding the determinant??
 2 years ago

inkyvoyd Group TitleBest ResponseYou've already chosen the best response.0
I'm wikipediaing, and not making any progress.
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
LOL. @ "wikipediaing" . :)
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
How to wolfram this ??
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@radar sir, any clue ??
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
factor out the commons!!!
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@experimentX , how exactly ?? I mean row wise or column wise. And moreover, what to factor out ??
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
lol ... factoring out would lead to 3 more matrices ..thats ugly... must be some pattern!!
 2 years ago

shivam_bhalla Group TitleBest 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 :)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
it seems transpose of itself!!
 2 years ago

apoorvk Group TitleBest ResponseYou've already chosen the best response.1
dw:1336584742255:dw this is how far i got then..
 2 years ago

experimentX Group TitleBest 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!!!
 2 years ago

shivam_bhalla Group TitleBest 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
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
if you find let met know!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
Oo ...we can drop all ones!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
Oo ... i got zero!! LOL
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
@shivam_bhalla you still there??
 2 years ago

experimentX Group TitleBest 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}}
 2 years ago

shivam_bhalla Group TitleBest 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 :)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
No .. i know the shortcut too!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
actually i verified answer at wolframalpha!!
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
Ok. Just tell me the method and not the steps because that would literally troll you
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@experimentX
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
take out all ones!! sine they will have same values on row .. they will be zero ..
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
Sorry, didn't get you @experimentX
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
dw:1336588777520:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
dw:1336588827490:dw
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
dw:1336588893052:dw
 2 years ago

eigenschmeigen Group TitleBest 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
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
whenever matrix has same elements on row or column ... determinant is zero.
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
and by symmetry (bc) and (ac) are
 2 years ago

shivam_bhalla Group TitleBest 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 :)
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
proportional >eg R1 = kR2 so k = 1 is a specific case
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
Oo ... then i must have mistake!!
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
no its correct
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
if R1 = R2 then det(M) = 0
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@eigenschmeigen , there is no R1=R2 in @experimentX 's proof
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
Oh my mistake ... i got the answer in fluke
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@experimentX , I wish these flukes come for me too in my exam :P
 2 years ago

experimentX Group TitleBest 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!!
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
LOL. I have college entrance exam's right now :P
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
*exams
 2 years ago

eigenschmeigen Group TitleBest 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
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
The problem as of now is unsolved @eigenschmeigen
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
Okay ... i think i got this time!! you can use same technique to reduce matrix!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
dw:1336589808195:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
and then it's simplification!!
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
apply operation as above!!! dw:1336589933207:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
same as you had in your second place!!  minus  one
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
dw:1336590227531:dw
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.2
dw:1336590458004:dw It can be proved!!
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@experimentX , I will try and let you know in 510 minutes @experimentX
 2 years ago

experimentX Group TitleBest 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!!
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
its B
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
i'm just checking my working
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
how do i write matrices on here?
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
@eigenschmeigen , your answer is right. You can use drawing doard :)
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
ok gimme a sec
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
*board.
 2 years ago

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

eigenschmeigen Group TitleBest 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'
 2 years ago

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

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
factor out (ab)(bc)
 2 years ago

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

eigenschmeigen Group TitleBest 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
 2 years ago

eigenschmeigen Group TitleBest 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.
 2 years ago

eigenschmeigen Group TitleBest 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
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.0
Thank you @eigenschmeigen and @experimentX for both of your solutions :D Thanks for taking your time :)
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
no problem, love matrices :)
 2 years ago

experimentX Group TitleBest 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
 2 years ago

eigenschmeigen Group TitleBest ResponseYou've already chosen the best response.1
what else does linear algebra cover?
 2 years ago

experimentX Group TitleBest 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!!
 2 years ago
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