# Describe the position of the elements of a matrix.

• July 16th 2010, 08:33 AM
kkm
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?
• July 16th 2010, 08:36 AM
Ackbeet
Are you sure it's afj, or is it more like $A_{ij}$? Does square matrix of order two mean that it's a 2 x 2 matrix?
• July 16th 2010, 09:14 AM
kkm
Yes, the matrix is $A_{ij}$.

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

Sorry for the confusion.
• July 16th 2010, 09:15 AM
Ackbeet
So, you tell me, what does the i correspond to? And what does the j correspond to?
• July 16th 2010, 09:29 AM
kkm
Quote:

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.
• July 16th 2010, 09:38 AM
Ackbeet
So, which elements of the following matrix $A$ have row index = 2?

$A=\left[\begin{matrix}2 &5\\7 &3\end{matrix}\right].$
• July 16th 2010, 10:02 AM
kkm
Quote:

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

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

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:

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

To b:

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

To c:

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

Am I right?
• July 16th 2010, 10:05 AM
Ackbeet
For part a, you have correctly exhibited the elements there. How would you describe where those elements are in the matrix?

• July 16th 2010, 10:34 AM
kkm
Quote:

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

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

b) where $j = 1$:
$A_{11}$ with element 2
$A_{21}$ 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 $i = j$, so $i = 1$:

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

Why, isn't this right?

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

Then, of course, it would be:

$A_{11}$ 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...
• July 16th 2010, 10:44 AM
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.

For part c, i=j by no means forces i to equal 1. What if i=j=2? So which matrix elements are those?
• July 16th 2010, 11:24 AM
kkm
Quote:

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.

Quote:

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.

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

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.
• July 16th 2010, 11:26 AM
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.
• July 16th 2010, 11:39 AM
kkm
Quote:

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.