Question

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??

Answer 1

http://mypat.in/PaperImages/3/425/Q_4_004.gif

Answer 2

can you factor all of the elements

Answer 3

@UnkleRhaukus ,how exactly??

Answer 4

\[\Delta=\left|\begin{array}\\1+a^2+a^4&1+ab+a^2b^2&1+ac+a^2c^2\\1+ab+a^2b^2&1+b^2+b^4&1+bc+b^2c^2\\1+ac+a^2c^2&1+bc+b^2c^2&1+c^2+c^4\end{array}\right|\]

Answer 5

yeah maybe not, i really dont want to do it the normal way

Answer 6

Normal way-->never :D It would take ages :P

Answer 7

but it would work in theory, but i would make about ten mistakes

Answer 8

I am sure you play around with determinant properties like Row1 = Row 1 + Row 2+Row3 . I mean some tweaking of that sort

Answer 9

@apoorvk

Answer 10

can we just do it the foolish way?

Answer 11

Hmm, tried C1 - C2?

Answer 12

@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

Answer 13

@apoorvk , I did that. But nothing can be taken common out :(

Answer 14

I'm going to try this problem

Answer 15

Have no fear, for inky is here!

Answer 16

I got common stuff out through C1-C2 and C2-C3. but, i am still stuck with a trinomial in each ditch..

Answer 17

@shivam_bhalla I HAVE AN IDEA

Answer 18

aei+bfg+cdh-ceg-bdi-afh
=a(ei-fh)+b(fg-dj)+c(dg-eg)

Answer 19

b=d
f=h

Answer 20

c=g

Answer 21

aei+bfg+cdh-ceg-bdi-afh
aei+bf^2+cbf-ec^2-ah^2

Answer 22

@inkyvoyd , what is a,b,c,d,e,f,g?? Are you expanding the determinant??

Answer 23

I'm wikipediaing, and not making any progress.

Answer 24

LOL. @ "wikipediaing" . :)

Answer 25

wolfram!!!

Answer 26

How to wolfram this ??

Answer 27

@radar sir, any clue ??

Answer 28

factor out the commons!!!

Answer 29

@experimentX , how exactly ?? I mean row wise or column wise. And moreover, what to factor out ??

Answer 30

lol ... factoring out would lead to 3 more matrices ..thats ugly... must be some pattern!!

Answer 31

Oh. Now get what you meant by factoring .:P I tried that too and observed what you said :)

Answer 32

it seems transpose of itself!!

Answer 33

this is how far i got then..