Question

Linear algebra help, please! (last time, my computer froze)

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 \[\left[ x-> \right]_{B _{2}} = \left(\begin{matrix}-3 \\ 7\end{matrix}\right)\], what is x-> (Vector notation)

Answer 2

d) Find \[[\left(\begin{matrix}-3 \\ 7\end{matrix}\right)]_{B _{2}}\]

e) Let P be the change of basis matrix for which \[[x->]_{B _{1}} = P[x->]_{B _{2}}. \] Find P