Find the matrices of the following linear transformations from R3 to R3.
The orthogonal projection onto the xy-plaNE: (3X3)...
The reflection in the z-axis:(3X3)

The matrixes are in the explanation box.

1. A mapping of (x,y,z) to (x,y,0)

2. Is a mapping of (x,y,z) to (-x,-y,z)

Step-by-step explanation:

We have the orthogonal projection onto the cy-plane to be a mapping of (x,y,z) to (x,y,0). Then we will have a transformation matrix that has the form below.

[1 0 0]

[0 1 0]

[0 0 1]

For the reflection in the z-axis,it is a reflection of (x,y,z) to (-x,-y,z). Our matrix will then have the form below

[-1 0 0]

[0 -1 0]

[0 0  1]

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