Question

Find a basis for the subspace \begin{equation} W = \left\{ \begin{bmatrix} 2a + 5b & 6b \\ 4a & 9b \end{bmatrix} \in \mathbb{R}^{2 \times 2} \mid a, b \in \mathbb{R} \right\} \text{ of } \mathbb{R}^{2 \times 2}. \end{equation} A basis for $W$ is $\left\{ \begin{bmatrix} 1 & 0 \\ 4 & 0 \end{bmatrix}, \begin{bmatrix} \boxed{ } & 6 \\ \boxed{ } & \boxed{ } \end{bmatrix} \right\}$.

          Find a basis for the subspace
\begin{equation*}
W = \left\{ \begin{bmatrix} 2a + 5b & 6b \\ 4a & 9b \end{bmatrix} \in \mathbb{R}^{2 \times 2} \mid a, b \in \mathbb{R} \right\} \text{ of } \mathbb{R}^{2 \times 2}.
\end{equation*}
A basis for $W$ is $\left\{ \begin{bmatrix} 1 & 0 \\ 4 & 0 \end{bmatrix}, \begin{bmatrix} \boxed{ } & 6 \\ \boxed{ } & \boxed{ } \end{bmatrix} \right\}$.

$Find a basis for the subspace W = { < b m a t r i x > ∈ℝ^2 × 2| a, b ∈ℝ} of ℝ^2 × 2. A basis for W is { < b m a t r i x > , < b m a t r i x > }.$