Assignment:
Consider the following three vectors in R^3:
x_1=(1, -1, 0, 2)
x_2=( 1,1,1,0)
x_3= (-1,-1,2,0)
a) Verify that {x_1, x_2, x_3} are orthogonal with the standard inner product in R^4
b) Find a nonzero vector x_4 such that {x_1, x_2, x_3, x_4} is a set of mutually orthogonal vectors.
c) Convert the resulting set into an orthonormal basis for R^4
Provide complete and step by step solution for the question and show calculations and use formulas.