• dellatorre
In summary, the conversation was discussing how to take the cross product of two 3x3 matrices. However, it was determined that the cross product is not an operation on matrices. The original problem was then stated and the conversation shifted towards finding the equivalent matrix for a reflection about the line y=-x. It was suggested to multiply the matrices for the reflection relative to the y-axis and the counter-clockwise rotation of 90 degrees.
dellatorre
How do I take the cross product of Two 3x3 Matrices.

For example what is cross product of:
[-1 0 0]
[0 1 0]
[0 0 1]
x
[0 -1 0]
[1 0 0]
[0 0 1]

thanks,
Della

The cross product isn't an operation on matrices -- your question doesn't make sense as given. Can you provide more information?

ok, maybe its not the cross product I need to do then.

The problem I'm struggling with is this:
"Show that matrix
[0 -1 0]
[-1 0 0]
[0 0 1]
for a reflection about line y=-x
is equivalent to a reflection relative to the y-axis followed by a counter-clockwise rotation of 90 degrees."

So for my answer, first I have for the reflection relative to the y axis, I have the matrix:
[-1 0 0]
[0 1 0]
[0 0 1]

and for the counter-clockwise rotation of 90 degrees, I have the matrix:
[0 -1 0]
[1 0 0]
[0 0 1]

but then I don't know what my next step should be.

Do you know how to do this?

thanks,
Della

dellatorre said:
So for my answer, first I have for the reflection relative to the y axis, I have the matrix:
[-1 0 0]
[0 1 0]
[0 0 1]
That one changes the x coordinate of the vector it acts on, not the y coordinate.

dellatorre said:
but then I don't know what my next step should be.
Multiply the matrices.

Last edited:
thank you all :-))

1. What is a cross product of two 3x3 matrices?

The cross product of two 3x3 matrices is a mathematical operation that produces a new matrix by multiplying the corresponding elements of the two matrices and summing the results. This operation is only defined for matrices with the same dimensions, in this case, 3 rows and 3 columns.

2. Why would I need to perform a cross product of two 3x3 matrices?

The cross product of two 3x3 matrices is commonly used in linear algebra and 3D graphics to calculate transformations, rotations, and other operations. It can also be used to solve systems of linear equations and find the inverse of a matrix.

3. What are the steps to cross product two 3x3 matrices?

The steps to cross product two 3x3 matrices are as follows:

• Multiply the corresponding elements of the first row of the first matrix by the corresponding elements of the first column of the second matrix.
• Repeat this for the remaining rows and columns, multiplying and summing the results for each element of the resulting matrix.
• The resulting matrix will have the same dimensions as the original matrices, in this case, 3 rows and 3 columns.

4. Are there any special properties of the cross product of two 3x3 matrices?

Yes, the cross product of two 3x3 matrices is distributive and associative, meaning that the order in which the matrices are multiplied does not affect the result, and the operation can be broken down into smaller parts and then combined.

5. Are there any tools or software that can help with cross product of two 3x3 matrices?

Yes, there are several mathematical software programs available that can perform cross product operations, such as MATLAB, Mathematica, and Python's NumPy library. These tools can also handle larger matrices and provide additional functionalities for matrix operations.

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