# Thread: Describe the position of the elements of a matrix.

1. ## Describe the position of the elements of a matrix.

Given this problem:

In the square matrix «afj» of order two describe the position of the
elements. Where:
(a) i = 2
(b) j = 1
(c) i = j

This is an excerpt from my maths book. I do not understand what I exactly have to to do. Can you assist me with this one, please?

2. Are you sure it's afj, or is it more like $\displaystyle A_{ij}$? Does square matrix of order two mean that it's a 2 x 2 matrix?

3. Yes, the matrix is $\displaystyle A_{ij}$.

Yes, square matrix of order two means it's a 2 x 2 matrix.

Sorry for the confusion.

4. So, you tell me, what does the i correspond to? And what does the j correspond to?

5. Originally Posted by Ackbeet
So, you tell me, what does the i correspond to? And what does the j correspond to?
i refers to the matrix' row index.
j refers to the column index.

Still, I don't seem to understand the exercise. Thanks, for your time.

6. So, which elements of the following matrix $\displaystyle A$ have row index = 2?

$\displaystyle A=\left[\begin{matrix}2 &5\\7 &3\end{matrix}\right].$

7. Originally Posted by Ackbeet
So, which elements of the following matrix $\displaystyle A$ have row index = 2?

$\displaystyle A=\left[\begin{matrix}2 &5\\7 &3\end{matrix}\right].$
I think I know what you're trying to say and I will try to solve the exercise.

So, given your matrix, the solution to a would be:

$\displaystyle A_{21}$ with element 7
$\displaystyle A_{22}$ with element 3

To b:

$\displaystyle A_{12}$ with element 5
$\displaystyle A_{22}$ with element 7

To c:

$\displaystyle A_{11}$ with element 2
$\displaystyle A_{12}$ with element 5

Am I right?

8. For part a, you have correctly exhibited the elements there. How would you describe where those elements are in the matrix?

9. Originally Posted by Ackbeet
For part a, you have correctly exhibited the elements there. How would you describe where those elements are in the matrix?

I would say: "The elements are in the second row of the matrix A with order 2 x 2."

Correction

$\displaystyle A=\left[\begin{matrix}2 &5\\7 &3\end{matrix}\right].$

b) where $\displaystyle j = 1$:
$\displaystyle A_{11}$ with element 2
$\displaystyle A_{21}$ with element 7

I must have slept to get this wrong...

The position of the elements would be: "the second column of the matrix A with order 2 x 2".

c where $\displaystyle i = j$, so $\displaystyle i = 1$:

$\displaystyle A_{11}$ with element 2
$\displaystyle A_{12}$ with element 5

Why, isn't this right?

Or, does it mean where $\displaystyle i = 1$ and where $\displaystyle j = 1$?

Then, of course, it would be:

$\displaystyle A_{11}$ with element 2

The position would be: "the first column and row of the matrix A with order 2 x 2".

Is this right? I hope I am beginning to understand...

10. You've nailed part a. I think a statement such as "The elements are in the second row of the matrix A with order 2 x 2." is precisely what the problem is asking for. For part b, you've got the right idea, but not the correct details. It's not the second column, but the _______ column.

For part c, i=j by no means forces i to equal 1. What if i=j=2? So which matrix elements are those?

11. Originally Posted by Ackbeet
You've nailed part a. I think a statement such as "The elements are in the second row of the matrix A with order 2 x 2." is precisely what the problem is asking for. For part b, you've got the right idea, but not the correct details. It's not the second column, but the _______ column.
Oh, yes. Of course, it's the first column. My head must be somewhere, but not with me.

For part c, i=j by no means forces i to equal 1. What if i=j=2? So which matrix elements are those?
You're right. My presumption was false.

$\displaystyle A_{11}$ and
$\displaystyle A_{22}$ because $\displaystyle i = j$.

The position of the elements would be: "the row and column where the value of the row index equals the column index."
After writing it down it makes much more sense to me.

Oh, yes, I hope I get it right now.

12. Everything looks good. There is a name for the elements described by part c: the main diagonal. I think that's what the problem is after there.

13. Originally Posted by Ackbeet
Everything looks good. There is a name for the elements described by part c: the main diagonal. I think that's what the problem is after there.
OK.