WeBWorK Standalone Renderer

Suppose that $f: \mathbb{R}^2 \to \mathbb{R}^2$ is a linear transformation. The figure shows a basis $\mathcal{B} = \lbrace \mathbf{b_1}, \mathbf{b_2} \rbrace$ for $\mathbb{R}^2$ for the domain and codomain (in black), its $\mathcal{B}$ -coordinate grid in both the domain and the codomain (in gray), a vector $\mathbf{v}$ in the domain (in red), and vectors $f(\mathbf{b_1})$ and $f(\mathbf{b_2})$ in the codomain (in blue).

		$\Large \stackrel{\displaystyle \lbrack f \rbrack_{\mathcal{B}}^{\mathcal{B}}}{\to}$
$\mathcal{B}$ -coordinate grid				$\mathcal{B}$ -coordinate grid

Part 1: Geometric properties of the linear transformation

Write the vectors $f(\mathbf{b_1})$ and $f(\mathbf{b_2})$ as linear combinations of the vectors in the basis $\mathcal{B}$ . Enter a vector sum of the form 5 b1 + 6 b2.
$f(\mathbf{b_1}) =$
$f(\mathbf{b_2}) =$

The vector $\mathbf{b_1}$ an eigenvector for the linear transformation $f$ with eigenvalue (enter a number or DNE).
The vector $\mathbf{b_2}$ an eigenvector for the linear transformation $f$ with eigenvalue (enter a number or DNE).

Part 2: The matrix of the linear transformation relative to the basis B

Part 3: Evaluating the linear transformation

You can earn partial credit on this problem.