What Is the Line of Reflection for the Matrix Transformation f(v)?

AI Thread Summary
The discussion centers on finding the line of reflection for the matrix transformation f(v) defined by the given matrix. The transformation is shown to represent a reflection in a line L through the origin. To determine the line of reflection, one must identify a line L that remains fixed under the transformation f. Participants express difficulty in comparing the reflection formulas and identifying the fixed line. The key focus is on understanding the relationship between the matrix and the geometric reflection it represents.
bookworm_07
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f(v) = (the matrix)
|cosx sinx |
|sinx -cosx |(v)

If x is in R and f: R^2 --> R^2
show that f is a reflection in a line L through the origin, and find the line of reflection.

im having trouble figureing this out, i know that i need to find a line L fixed by f, and then to compare the formulas for the reflection --> RL and f.
i just don't know what to do. Thank you.
 
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