Question

How many symmetric matrices can be obtained by using
0,0,0,0,0,-1,-1,1,1

Answer 1

3

Answer 2

ooh nope, it's more

Answer 3

yup,its not 3

Answer 4

6, the 1's have to be on a diagonal

Answer 5

I don't have answer for this one,I have a similar question with the correct answer so I am changing the values,tell now

Answer 6

ooops. 6 isn't enough either...

Answer 7

stop guessing :|

Answer 8

okay, both 2's or none can be on the diagonal. likewise, two 0's or none on the diagonal. so one 1 or all three 1's must be on a diagonal.
right?

Answer 9

I changed the values! there are no 2's now,this is easier.

Answer 10

2(6+9+9) = 48

Answer 11

wrong again

Answer 12

what is it?

Answer 13

sorry, duplicates when 0 is in the 2,2 position

Answer 14

Its 12.

Answer 15

\[\left[\begin{matrix}0 & 0 & -1 \\0 & 0 & 1\\ -1 &1 & 0\end{matrix}\right] \left[\begin{matrix}0 & 0 & 1 \\0 & 0 & =1\\ 1 &=1 & 0\end{matrix}\right]\]

\[\left[\begin{matrix}0 & 1 & -1 \\1 & 0 & 0\\ -1 &0 & 0\end{matrix}\right] \left[\begin{matrix}0 & -1 & 1 \\-1 & 0 & 0\\ 1 &0 & 0\end{matrix}\right]\]

\[\left[\begin{matrix}0 & 1 & 0 \\1 & 0 & -1\\ 0 &-1 & 0\end{matrix}\right] \left[\begin{matrix}0 & -1 & 0 \\-1 & 0 & 1\\ 0 &1 & 0\end{matrix}\right]\]

\[\left[\begin{matrix}0 & 0 & 0 \\0 & 1 & -1\\ 0 &-1 & 1\end{matrix}\right] \left[\begin{matrix}0 & -1 & 0 \\-1 & 1 & 0\\ 0 &0 & 1\end{matrix}\right]\left[\begin{matrix}0 & 0 & -1 \\0 & 1 & 0\\ -1 &0 & 1\end{matrix}\right]\]

\[\left[\begin{matrix}1 & 0 & 0 \\0 & 0 & -1\\ 0 &-1 & 1\end{matrix}\right] \left[\begin{matrix}1 & -1 & 0 \\-1 & 0 & 0\\ 0 &0 & 1\end{matrix}\right]\left[\begin{matrix}1 & 0 & -1 \\0 & 0 & 0\\ -1 &0 & 1\end{matrix}\right]\]

\[\left[\begin{matrix}1 & 0 & 0 \\0 & 1 & -1\\ 0 &-1 & 0\end{matrix}\right] \left[\begin{matrix}1 & -1 & 0 \\-1 & 1 & 0\\ 0 &0 & 0\end{matrix}\right]\left[\begin{matrix}1 & 0 & -1 \\0 & 1 & 0\\ -1 &0 & 0\end{matrix}\right]\]

\[\left[\begin{matrix}0 & 0 & 0 \\0 & -1 & 1\\ 0 & 1 & -1\end{matrix}\right] \left[\begin{matrix}0 & 1 & 0 \\1 & -1 & 0\\ 0 &0 & -1\end{matrix}\right]\left[\begin{matrix}0 & 0 & 1 \\0 & -1 & 0\\ 1 &0 & -1\end{matrix}\right]\]

\[\left[\begin{matrix}-1 & 0 & 0 \\0 & 0 & 1\\ 0 &1 & -1\end{matrix}\right] \left[\begin{matrix}-1 & 1 & 0 \\1 & 0 & 0\\ 0 &0 & -1\end{matrix}\right]\left[\begin{matrix}-1 & 0 & 1 \\0 & 0 & 0\\ 1 &0 & -1\end{matrix}\right]\]

\[\left[\begin{matrix}-1 & 0 & 0 \\0 & -1 & 1\\ 0 &1 & 0\end{matrix}\right] \left[\begin{matrix}-1 & 1 & 0 \\1 & -1 & 0\\ 0 &0 & 0\end{matrix}\right]\left[\begin{matrix}-1 & 0 & 1 \\0 & -1 & 0\\ 1 &0 & 0\end{matrix}\right]\]

ummm. it's more than 12

Answer 16

Assign the 1s, then assign the -1s... the zeroes will fill the remaining parts in.

Answer 17

Also, since it is symmetric, only assign the bottom left of the triangle..

Answer 18

Yeah,@wio the solution is something like that,but I need a little detailed explanation..just one example of how we do it,like for one matrix..

Answer 19

@terenzreignz @oldrin.bataku

Answer 20

Do you know what a symmetric matrix is?

Answer 21

\[\Huge a_{ij}=a_{ji} \]
\[\Huge [A]'=[A]\]

Answer 22

Good! So we are given 5 zeros, 2 negative ones, and 2 ones
And we are asked to arrange this set of numbers into symmetric matices?

Answer 23

Absolutely :)

Answer 24

And we are looking for the number of symmetric matrices, right?

Answer 25

Ok. The first thing to do is determine the size of the matrix.

Answer 26

@DLS Like you said, for a symmetric matrix, we need matrix A to equal the transpose matrix A(T)

Answer 27

@DLS if this is the case, what can you tell me about the size of the matrix?

Answer 28

Yes

Answer 29

hat can you tell me about the size of the matrix?

Answer 30

what*

Answer 31

3x3

Answer 32

Right!

Answer 33

Ok, let's set up a generic 3x3 matrix and it's transpose and see if we can go from there.