we choose a basis B={v1=(1,0)v2=(1,1)} from $\displaystyle R^2$

and define $\displaystyle (x,y)_B=x_1y_1+x_2y_2$

why does the prof say that

$\displaystyle x=x_1v_1+x_2v_2$

$\displaystyle y=y_1v_1+y_2v_2$

how did he get those formulas?

and i cant se the structure of our chosen basis here?

how to see it in thos formulas

?