4. Suppose T: R³ -> R³ is the linear transformation defined by

Which is the following is equal to

A

B

C

D

E does not exist

Solution: The answer is B.

The inverse in question is the (x, y, z) that satisfy the system of equations

You could solve this for x, y and z, and eventually arrive at the answer. But, notice that since x + z = 3, a simple mental computation shows that A and B are the only possible answers. Next, since x + 3y = 2, the only possibility is B. As a final verification, check that x + y + 2 z =1.