\[
\displaylines{\text{Given a basis }B=\left\lbrace\left(1,2\right),\left(3,4\right)\right\rbrace\text{ and }\mathbf{v}=\left(1,0\right)\\ 1)\text{ Determine }\left\lbrack\mathbf{v}\right\rbrack_{B}\\ 2)\text{ Find }P_{B}\text{ (The change of coordinates matrix from B-coordinates to standard basis)}}
\]