Consider the following. {(1, −6, 3, 2), (1, 2, 0, 6)}
(a) determine whether the set of vectors in rn is orthogonal.
(b) if the set is orthogonal, then determine whether it is also orthonormal.
(c) determine whether the set is a basis for rn.

 The required answers are

(a) NOT orthogonal.

(b) NOT orthonormal.

(c) Not a basis,

Step-by-step explanation:  We are given to consider the vectors {(1, −6, 3, 2), (1, 2, 0, 6)}.

(a) We are to determine whether the set of vectors in is orthogonal.

(b) If the set is orthogonal, then to determine whether it is also orthonormal.

(c) To determine whether the set is a basis for .

We know that

any two vectors u and v are orthogonal, if their dot product u.v is zero.

The dot product of (1, −6, 3, 2) and (1, 2, 0, 6) is given by

So, the given set is not orthogonal.

Since the vectors are not orthogonal, they cannot be orthonormal.

To be a basis of , the set must contain n vectors.

Here, we are dealing with and the set contains only 2 vectors.

So, the given set cannot be a basis.

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