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