Suppose is a linear transformation defined by and . Then the standard matrix for this linear transformation is:

A mapping is said to be onto if each in is the image of at least one in . Decide which of the following transformations is onto.

where

onto not onto

where

onto not onto

where

onto not onto
True/False: Let be a linear transformation. Then is one-to-one if and only if the equation has only the trivial solution.
True False
Decide which of the following transformations is one-to-one. (Hint: Use the true/false statement above.)

where

one-to-one not one-to-one

where

one-to-one not one-to-one

where

one-to-one not one-to-one