Answer
Since the set is not orthogonal, the set of vectors is not orthonormal.
Work Step by Step
Note: Vectors can be rewritten using <>, so
$u_{1}$ = <0, 1, 0>
$u_{2}$ = <0, -1, 0>
A set of vectors is orthonormal if the set is orthogonal and if each of the vectors is a unit vector. To determine if the set is orthonormal we must first determine if the set is orthogonal, and then we need to determine if each vector is a unit vector.
1. Determine if the set of vectors is orthogonal.
Note: To determine if a set is orthogonal, each pair of vectors must be orthogonal meaning the dot product = 0.
In this case, $u_{1}$∙$u_{2}$ must equal 0 to be orthogonal.
$u_{1}$∙$u_{2}$ = <0, 1, 0>∙<0, -1, 0> = (0)(0) + (1)(-1) + (0)(0) + 0 + (-1) + 0 = -1
Since $u_{1}$∙$u_{2}$ $\ne$ 0, the pair is not orthogonal. Since there is only one pair, the set is not orthogonal.
Note: Since the set it not orthogonal, we do not need to see if the vectors are unit vectors because one of the conditions was not met.
Since the set is not orthogonal, the set of vectors is not orthonormal.
