Answer
See below
Work Step by Step
According to Gram-Schmidt process, we have:
$v_1=x_1=(1,2,3,4,5)\\
v_2=x_2-\frac{}{||v_1||^2}v_1\\
=(-7,0,1,-2,0)-\frac{)}{||(1,2,3,4,5)||^2}(1,2,3,4,5)\\
=(-7,0,1,-2,0)-\frac{(-7).1+2.0+1.3+(-2).4+0.5}{1^2+2^2+3^2+4^2+5^2}(1,2,3,4,5)\\
=(-7,0,1,-2,0)-\frac{-7+0+3-8+0}{1+4+9+16+25}(1,2,3,4,5)\\
=(-7,0,1,-2,0)+\frac{22}{55}(1,2,3,4,5)\\
=\frac{1}{55}(-373,24,91,-62,60)$
To determine an orthogonal set, we obtain:
$\frac{v_1}{||v_1||}=\frac{(1,2,3,4,5)}{\sqrt 1^2+2^2+3^2+4^2+5^2}=\frac{(1,2,3,4,5)}{\sqrt 55}=\frac{1}{\sqrt 55}(1,2,3,4,5)$
$\frac{v_2}{||v_2||}=\frac{\frac{1}{55}(-373,24,91,-62,60)}{\frac{1}{55}\sqrt 155430}=\frac{1}{\sqrt 155430}(-373,24,91,-62,60)$
