Answer
True
Work Step by Step
If $B_1=\{x_1,x_2\}\\
B_2=\{2x_1,2x_2\}$
Apply Gram- Schmidt process:
$w_1=2x_1=2v_1\\
w_2=2x_2-\frac{<2x_2,w_1>}{||w_1||^2}w_1\\
=2x_2-\frac{<2x_2,w_1>}{}w_1\\
=2x_2-\frac{<2x_2,2v_1>}{<2v_1,2v_1>}2v_1\\
=2x_2-\frac{2.2}{2.2}2v_1\\
=2x_2-2\frac{}{||v_1||^2}v_1\\
=2(x_2-\frac{}{||v_1||^2}v_1)\\
=2v_2$
Apply the Gram-Schmidt Process to $B_2 =\{2x_1, 2x_2\}$ will yield
the orthogonal set $\{2v_1, 2v_2\}$
