Question

Linear Help please! It's about bases! Fun stuff!

Answer 1

Let \[B _{1} = \left\{ \left(\begin{matrix}1 \\ -2\end{matrix}\right), \left(\begin{matrix}-3 \\ 7\end{matrix}\right) \right\} and B _{2} = \left\{ \left(\begin{matrix}2 \\ 5\end{matrix}\right) ,\left(\begin{matrix}1 \\ 4\end{matrix}\right) \right\}\].
a) Both of the sets B_i are bases of R^2. Prove that B1 is a basis.
b) If \[[x->]_{B _{2}} = \left(\begin{matrix}-3 \\ \end{matrix}\right)\] what is x->? (Vector notation)