Question

Anyone know how to do this?


Determine an orthonormal basis of the subspace U  R4 which is
spanned by the three vectors u1 = (1, 2, 2, 0), u2 = (−1, 3, 2, 2), u3 = (1, 1, 3, 5).

Answer 1

@Sportaholic013 A basis set is a spanning set that is linearly independent. A basis can be formed in any real vector space. Any two basis of the same vector space have equal number of members. The number of elements or members in a basis of a vector is the dimension of the vector.

In case you don't know what I mean by linearly independent, allow me explain. If the only linear combination of all the vectors in a given a vector space {v[1], v[2], v[3], v[4], ..., v[n]} thet produces the zero vector is 0v[1] + 0v[2] + 0v[3] + 0v[4] + ... + 0v[n], then the vectors are linearly independent. In other words, all the scalars must be zero.