Math Community Quiz

[Xeda112358]

Hehehe, mwahahahaha. Eh-zactly. So I wonder what magic this next question will perform...?

[jnesselr]

Given a square matrix M (2 x 2 matrix), and it's determinant, and that some matrix K multiplies by M gives the 2 x 2 matrix N, find K.

You are given det(M)=12.  All values in M are prime.
You are given det(K)=-1316.  All values but one in K are prime.
You are given N=[ [ 252 , 1792 ] [ 384 , 2668 ] ]

Knowing the matrix K multiplied times the matrix M = N, find K and M.

[nemo]

that's eerie. i found 1316 matrices which are all prime and have the determinant -1316. working on the other part though. (between the primes 2-499 that is)

[jnesselr]

that's eerie. i found 1316 matrices which are all prime and have the determinant -1316. working on the other part though. (between the primes 2-499 that is)

Yep, that sounds about right.  I have two matrixes that I have, but I think there might be an infinite number of them.  Who knows.

[nemo]

i just tried prime numbers under 1000, found 3868 matrices with a -1316 determinant and 6366 with a 12 as its determinant. should i have found two that multiply together to get N by now?

and it doesnt work up to 2000, i get the feeling going higher is useless, and i probably have a bug in my program somewhere i can't find. i feel kind of bad making java loop a hundred million times.

[jnesselr]

Has anyone made any progress on this?

[ruler501]

i'm working just not having much time trying to learn C++ and my compiler won't work so reinstalling it and my IDE.
Have Algebra work and English Homework
I'm making a little headway should be done soon if I have time to work on it

[nemo]

Has anyone made any progress on this?

i'm just waiting for you to tell me if i should find the matrix within the first 1000 primes. i.e. i took all the matrices comprised of the first 1000 times whose determinant is 12 and multiplied them by all the matrices comprised of the first 1000 times whose determinant is -1316, and i still didn't get a product of N. is my program broke? or is it larger than that (in which case, i'm not wasting 10 minutes of my time waiting on the JVM to multiply primal matrices.)

[ruler501]

I thought that was a bug in my program I didn't get any either.
graphmastur are there any under 1000 if not how high do we need to set the upper limit

[jnesselr]

Actually, every prime is under 100.

EDIT: People seem to be having difficulty with this, and I've gone over all the math, and I see why.

N=MK, not KM.
KM=[ [ 1832 , 1636 ] [ 1228 , 1088 ] ]
MK=[ [ 252 , 1792 ] [ 384 , 2668 ] ]

[nemo]

Actually, every prime is under 100.

that's good to know, now my program executes quickly... but to no avail, i cannot find the two matrices.

[jnesselr]

Actually, every prime is under 100.

that's good to know, now my program executes quickly... but to no avail, i cannot find the two matrices.

See my post edit just above yours.

[nemo]

Actually, every prime is under 100.

that's good to know, now my program executes quickly... but to no avail, i cannot find the two matrices.

See my post edit just above yours.

one step ahead of you, i anticipated that possibility and already ran my program for KM, MK, KK and MM. could you define 2x2 matrix multiplication for us?

Code: [Select]

[2, 5]   *   [11, 29]   =  [87 , 143]
[7, 9]       [13, 17]      [194, 356]

is this correct matrix multiplication?

[jnesselr]

Actually, every prime is under 100.

that's good to know, now my program executes quickly... but to no avail, i cannot find the two matrices.

See my post edit just above yours.

one step ahead of you, i anticipated that possibility and already ran my program for KM, MK, KK and MM. could you define 2x2 matrix multiplication for us?

Code: [Select]

[2, 5]   *   [11, 29]   =  [87 , 143]
[7, 9]       [13, 17]      [194, 356]

is this correct matrix multiplication?

Yes, that is the correct way to do matrix multiplication.

[nemo]

alright, this is the closest i've come.

Code: [Select]

K:
[ 5 ][ 83 ]
[ 17 ][ 19 ]

M:
[ 13 ][ 11 ]
[ 19 ][ 17 ]

Product M * K:
[ 252 ][ 1288 ]
[ 384 ][ 1900 ]


i found 8 matrices which had 2668 as their last element (both MK and KM).