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othronormal basis

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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

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This solution encompasses an othronormal basis.

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We consider the following three vectors in .
, , .
(a) We verify that the three vectors are mutually orthogonal to each ...

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