# othronormal basis

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

https://brainmass.com/math/geometry-and-topology/othronormal-basis-432749

#### Solution Preview

We consider the following three vectors in .

, , .

(a) We verify that the three vectors are mutually orthogonal to each ...

#### Solution Summary

This solution encompasses an othronormal basis.

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