Chapter 6.CR, Problem 101CR

To determine

(a)

The given statement “In calculus, any linear function is also a linear transformation from $R^2$ to $R^2$.” is true or false, if true provide the appropriate statement and if false provide the appropriate example.

To determine

(b)

The given statement “A linear transformation is onto if and only if, for all u and v in V, $T\left(\text{u}\right)=T\left(\text{v}\right)$ implies $\text{u}=\text{v}$” is true or false, if true provide the appropriate statement and if false provide the appropriate example.

To determine

(c)

The given statement, “For ease of computation, it is best to choose a basis for V such that the transformation matrix is diagonal” is true or false, if true provide the appropriate statement and if false provide the appropriate example.