Proving Matrix Expressions: AX = XA

In summary, the conversation is about a question regarding a matrix expression and how to show that it satisfies a certain condition. There is confusion over the presence of an "s" in the hypothesis and whether or not it was correctly typed.
  • #1
Mathman23
254
0
Hi

I got a question regarding a matrix expression:

Let [tex] X \in Mat_{n,n} (\mathbf{F}) [/tex]. Then I'm suppose to show AX = XA for all [tex]A \in Mat_{n,n} \mathbf{(F)}[/tex] if and only if [tex]s \in \mathbf{F}[/tex]

What is the best way of going about this?

/Fred
 
Last edited:
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  • #2
Did you miswrite something? What matrix expression?
 
  • #3
No, It is correctly typed.

/Fred

HallsofIvy said:
Did you miswrite something? What matrix expression?
 
  • #4
You did mistype something. s appears in the last three symbols and nowhere before, and the X vanishes from the question.
 
Last edited:
  • #5
When I first looked at it there was no matrix expression! May have been the server was slow in loading the LATEX. However, as Matt said, "if and only if [tex]s \in \mathbf{F}[/tex] makes no sense as there is no "s" in the hypothesis.
 

1. What is a matrix?

A matrix is a rectangular array of numbers or symbols arranged in rows and columns. It is commonly used in mathematics and science to represent and manipulate data.

2. What is a matrix expression?

A matrix expression is a mathematical statement that involves matrices and their operations, such as addition, subtraction, and multiplication.

3. What does the equation AX = XA mean?

The equation AX = XA means that the matrix A commutes with the matrix X. This means that the order of multiplication between A and X does not matter, and the resulting product will be the same.

4. How do you prove a matrix expression?

To prove a matrix expression, you need to show that both sides of the equation result in the same matrix when multiplied. This can be done by expanding the matrices and showing that the resulting entries are equal.

5. Why is proving matrix expressions important?

Proving matrix expressions is important because it allows us to validate mathematical statements and understand the relationships between matrices. It also helps us solve problems and make predictions in various fields, such as physics, engineering, and computer science.

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