# Homework Help: Confused about drawing matrix diagram

1. Feb 6, 2012

### tonic16

1. The problem statement, all variables and given/known data
Give an example of the matrix:
3x3 upper triangular symmetric matrix

2. Relevant equations

3. The attempt at a solution
I know what an upper triangular matrix and what a symmetric matrix looks like. But what happens when they put it together? Is the symmetry in the upper right portion of the matrix now? Like this?

1 5 3
0 2 5
0 0 3

2. Feb 6, 2012

### Staff: Mentor

What is the definition of a symmetric matrix?

3. Feb 6, 2012

### tonic16

Numbers are equal across the diagonal.

4. Feb 6, 2012

### Staff: Mentor

Which diagonal is that?

5. Feb 6, 2012

### tonic16

Middle diagonal like this:

1 2 4
2 3 7
4 7 5

6. Feb 6, 2012

### Staff: Mentor

Yes, and that's often called the main diagonal. So if a 3x3 matrix is symmetric and upper triangular, then a12 has to equal a21, for example. Since it is upper triangular, what must a21 equal?

7. Feb 6, 2012

### tonic16

So you are implying that the symmetric in this this case wouldn't even matter at all since there is upper triangular in it?

Answer should be something like this?

1 2 4
0 3 7
0 0 5

8. Feb 6, 2012

### Staff: Mentor

No, I am not saying that. Your matrix in post #7 is not symmetric, because a12 = 2, while a21 = 0.

Maybe you have a flawed understanding of what "upper triangular" means. How do you define this term?

9. Feb 6, 2012

### tonic16

Upper triangular would have zeros everywhere southwest of the main diagonal

10. Feb 6, 2012

### Staff: Mentor

And if such a matrix is also symmetric, what can you conclude?