Finding [L] for Two Consecutive Linear Transformations in R3

[lina29]

Homework Statement

A- Find [L] for L : R3 → R3 where L first reflects through the plane x−z = 0
and then rotates the zy-plane by pi/6 counterclockwise starting from the y-axis.

B-Find [L] for L : R3 → R3 where L first rotates the xy-plane by pi/4 counterclockwise starting from the x-axis and then reflects through the plane x + y − z = 0.

Homework Equations

The Attempt at a Solution

To be honest I don't really know where to start off on this problem. Any help would be appreciated. Thanks!

 

[I like Serena]

Hi lina29!

You need to think up a couple of vectors for which you can find the image.
For instance, for the reflection in a plane, you know that a vector in the plane will be transformed to itself.

Can you find 3 independent vectors and their transformations?

To make it easier for A, you can do this separately for both transformations, find the corresponding matrices, and multiply the matrices.
Or if you are up to the challenge, you can try to combine both transformations at once.