Answer
The set $\{(2,-4),(2,1)\}$ orthogonal, orthonormal and it is a basis for $R^2$
Work Step by Step
given $\{(2,-4),(2,1)\}$
let $v_1=(2,-4) , v_2=(2,1)$
(a)
since $v_1 v_2=4-4=0$
then, the space $\{(2,-4),(2,1)\}$ is orthogonal.
(b)
scince
$\left\|\mathbf{v}_{1}\right\|=\sqrt{\mathbf{v}_{1} \cdot \mathbf{v}_{1}}=\sqrt{4+16}=\sqrt{20}\neq1$
then, the space {(2,−4),(2,1)} is not orthonormal.
(c)
by the corollary to Theorem 5.10,$\{(2,-4),(2,1)\}$ is a basis for $R^2$
