- #1
joedozzi
- 20
- 0
Homework Statement
Homework Equations
The Attempt at a Solution
-(y, x) = -(YX-XY)
= XY-YX
Can I do this or would I have to define a matrix X= ( a b c d ) Y= ( e f g h)
And prove it that way? I am just really confused
Can I prove matrix properties using simple steps?
For example, the first step uses the definition of [X, Y] and the definition of matrix multiplication. The second step uses the distributive property. The third step uses the fact that -(A - B) = -A + B. The fourth step uses the definition of [Y, X] and the definition of matrix multiplication.
-(y, x) = -(YX-XY)
= XY-YX
Can I do this or would I have to define a matrix X= ( a b c d ) Y= ( e f g h)
And prove it that way? I am just really confused
- #2
Mark44
Mentor
- 37,659
- 9,914
joedozzi said:
What you have above would work, but your notation is awful! Try to use the notation as given in the problem. Also notice that uppercase letters represent matrices, and lowercase letters represent the entries in a matrix.
Assuming that matrices X and Y are in M, then [X, Y] = ?
Keep working with the expressions you get until you end up with -[Y, X].
- #3
joedozzi
- 20
- 0
[X, Y]= YX- XY
Thus [Y, X]= XY- YX
then -[Y, X]= -(XY- YX)
then -[Y, X]= -XY +YX
Like that? So i don't have to use matricies with variables, just use X and Y to represent a matrix?
Thus [Y, X]= XY- YX
then -[Y, X]= -(XY- YX)
then -[Y, X]= -XY +YX
Like that? So i don't have to use matricies with variables, just use X and Y to represent a matrix?
- #4
Mark44
Mentor
- 37,659
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joedozzi said:
This is easier to follow.
[X, Y] = XY - YX = -(YX - XY) = -[Y, X]
Can you say why each pair of successive equal expressions is valid?
- #5
joedozzi
- 20
- 0
Properties of Matricies?
- #6
joedozzi
- 20
- 0
And Thanks your honestly a huge help!
- #7
Mark44
Mentor
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That's pretty vague. Also, there are a number of steps. One reason doesn't fit them all.joedozzi said:
Related to Can I prove matrix properties using simple steps?
1. What are matrices used for in proofs?
Matrices are commonly used in proofs to represent systems of equations or transformations. They allow for a more organized and efficient way of solving mathematical problems involving multiple variables.
2. How do you know when to use a matrix in a proof?
You should use a matrix in a proof when the problem involves multiple equations or variables. This is because matrices can represent these equations in a more compact and organized manner, making it easier to solve the problem.
3. Can matrices be used to prove geometric concepts?
Yes, matrices can be used to prove geometric concepts such as rotations, reflections, and translations. Matrices are commonly used in linear algebra, which is a branch of mathematics that deals with vector spaces and geometric transformations.
4. What is the difference between a square matrix and a non-square matrix?
A square matrix has the same number of rows and columns, while a non-square matrix has a different number of rows and columns. Square matrices are typically used to represent systems of equations, while non-square matrices are used for transformations or other applications.
5. How do you perform operations on matrices in a proof?
To perform operations on matrices in a proof, you can use properties such as addition, subtraction, and multiplication. These operations can help you manipulate the matrices to solve the problem at hand.
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