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Linear Algebra Matrix Proof

  • Thread starter TJ@UNF
  • Start date
  • #1
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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

 

Answers and Replies

  • #2
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What did you try already?
 
  • #3
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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
4
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Oh ok. That's seems fairly obvious now. Thanks for your help.
 

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