Select all of the linear transformations from R3 to R3 that

Select all of the linear transformations from R^3 to R^3 that are invertible A. Reflection in the yz-plane B. Dilation by a factor of 2 C. Projection onto the y-axis D. Identity transformation: T(v) = nu for all nu E. Rotation about the z-axis by pi F. Projection onto the xz-plane

Solution

A. Invertible

Reflection about yz plane sends x to -x

So reflection about yz plane is its own inverse

B. Invertible

Dilation by factor of 1/2 is inverse of this transformation

C. Not Invertible

Because this is not one to one

eg.

(1,1,0) maps to (0,1,0)

(1,1,1) maps to (0,1,0)

D. Invertible

Identity transformation is its own inverse

E. Invertible

THis is its own inverse

F. Not invertible

(1,1,1) and (1,0,1) both map to (1,0,1)

Hence not one to one and hence not invertible map