Is matrix A diagonal, symmetric, or skew symmetric?

In summary, the given 3x3 matrix A has entries given by i/j and appears to be a diagonal matrix, where aij = 0 if i != j. The matrix is written as:1/1 1/2 1/32/1 2/2 2/33/1 3/2 3/3It is not specified if the matrix is symmetric, skew symmetric, or neither.
  • #1
TJ@UNF
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Homework Statement



Let A be a 3x3 matrix such that the ij-entry of A is given by i/j. write the matrix. Determine if A is Diagonal, symmetric, skew symmetric, or none of these.

I'm having trouble with this question. I would appreciate anyone's suggestions or input.

Thanks.


Homework Equations





The Attempt at a Solution

 
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  • #2
What did you try already?
 
  • #3
I'm not sure how to interpret the ij-entry given by i/j.

a11 a12 a13

A = a21 a22 a23

a31 a32 a33

and if it's given by i/j, does that mean I should think of the 3x3 matrix as

a1 a1/2 a1/3

a2 a1 a2/3

a3 a3/2 a1

If that's correct then it appears to have properties of a diagonal matrix where aij = 0 if i != j

I'm new to Linear Algebra so any input would be appreciated.
 
  • #4
The matrix would look like

1/1 1/2 1/3

2/1 2/2 2/3

3/1 3/2 3/3
 
  • #5
Oh ok. That's seems fairly obvious now. Thanks for your help.
 

1. What is a matrix?

A matrix is a rectangular array of numbers or symbols arranged in rows and columns.

2. What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of linear systems and their properties, including vectors, matrices, and linear transformations.

3. What is a proof in linear algebra?

A proof in linear algebra is a rigorous and logical demonstration of the validity of a mathematical statement or theorem using the rules and principles of linear algebra.

4. How do you prove a matrix is invertible?

To prove a matrix is invertible, you need to show that its determinant is non-zero. This can be done by using elementary row operations to reduce the matrix to its reduced row echelon form and checking that all its pivot entries are non-zero.

5. What is the purpose of proving properties of matrices in linear algebra?

The purpose of proving properties of matrices in linear algebra is to establish the fundamental rules and principles that govern the behavior of matrices, which are essential in solving linear systems and other mathematical problems.

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