Exercise 4.4.10

(a) If $q_1,q_2,q_3$ are orthonormal then the dot product of $q_1$ with $c_1{q}_1+c_2{q}_2+c_3{q}_3=$ $0$ gives $c_1=0$. Similarly $c_2=c_3=0$. This proves : Independent $q$ ’s

(b) $Qx=0$ leads to $Q^{T}Qx=0$ which says $x=0$.