## Elementary Linear Algebra 7th Edition

(a) the set is orthogonal. (b) the set is not orthonormal. (c) the set is not a basis for $R^3$.
Let $u=(2,5,-3)$ and $v=(4,2,6)$, then we have (a) since $u\cdot v=8+10-18=-0$, then the set is orthogonal. (b) since $\|u\|=4+25+9=38\neq 1$, then the set it is not orthonormal. (c) sine $R^3$ has dimension $3$ and the set has two vectors, then it is not a basis for $R^3$.