2.88 How to use GramSchmidt to find a set of orthonomal vectors?

Given set of linearly independent vectors \(V_1=[3,0,0],V_2=[0,1,2],V_3=[0,2,5]\), use GramSchmidt to find 3 orthonormal vectors from this set.

2.88.1 Mathematica

v1={3,0,0}; 
v2={0,1,2}; 
v3={0,2,5} 
Orthogonalize[{v1, v2,v3}, Method -> "GramSchmidt"]
 

\[ \left ( \begin {array}{ccc} 1 & 0 & 0 \\ 0 & \frac {1}{\sqrt {5}} & \frac {2}{\sqrt {5}} \\ 0 & -\frac {2}{\sqrt {5}} & \frac {1}{\sqrt {5}} \\ \end {array} \right ) \]

2.88.2 Maple

restart; 
V1:=Vector([3,0,0]); 
V2:=Vector([0,1,2]); 
V3:=Vector([0,2,5]); 
Student:-LinearAlgebra:-GramSchmidt([V1,V2,V3])
 

\[ \left [\left [\begin {array}{c} 1 \\ 0 \\ 0 \end {array}\right ], \left [\begin {array}{c} 0 \\ \frac {\sqrt {5}}{5} \\ \frac {2 \sqrt {5}}{5} \end {array}\right ] , \left [\begin {array}{c} 0 \\ -\frac {2 \sqrt {5}}{5} \\ \frac {\sqrt {5}}{5} \end {array}\right ] \right ] \]