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Let $f : \mathbb{R}^{2} \to \mathbb{R}^{3}$ be the linear transformation determined by $f(\vec{x}) = A \vec{x}$ where

$\displaystyle{A={\left[\begin{array}{cc} 3 &2\cr -2 &1\cr 0 &0 \end{array}\right]}.}$

1. For each of the following vector spaces,

if the space has a basis then enter a list of vectors that form a basis for the space. Separate basis vectors with commas if the basis has more than one vector . vector

(Remember: basis vectors must be linearly independent.)

a) Basis for $\mathrm{Kernel}(f)$ ?

b) Basis for $\mathrm{Image}(f)$ ?

2. The dimension of the kernel of $f$ is .

3. The dimension of the image of $f$ is .

4. The linear transformation ( f ) is

injective
surjective
bijective
none of these

You can earn partial credit on this problem.