Question

Let be the linear transformation that first projects points onto the -plane and then reflects around the line . Find the standard matrix for .

Answer 1

To find the standard matrix for the given linear transformation, we can multiply the standard matrices for the individual transformations.

Step-by-step explanation:

To find the standard matrix for the linear transformation that first projects points onto the xy-plane and then reflects around the line y = x, we can begin by considering the effect of each transformation separately.

First, let's consider the projection onto the xy-plane. This transformation simply erases the z-coordinate of a point, so we can represent it with the matrix [1 0 0; 0 1 0; 0 0 0].

Next, let's consider the reflection around the line y = x. This reflection swaps the x and y coordinates of a point, so we can represent it with the matrix [0 1 0; 1 0 0; 0 0 1].

To combine these transformations, we can multiply the two matrices. Using matrix multiplication, we get the standard matrix for the given linear transformation: [0 1 0; 1 0 0; 0 0 0].