Perform the GramSchmidt process on the following sequence of

Perform the Gram-Schmidt process on the following sequence of vectors.

$\"x=\"$

$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$	2	$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$
4
4

, $\"y=\"$

$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$	-1	$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$
1
4

, $\"z=\"$

$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$	2	$\"\\left.\\vphantom{\\begin{array}{c}\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\!\\strut\\\\\\end{array}}\$
-5
-5

x = ( 2, 4 ,4 ) ; y = ( -1 , 1 , 4) and z = ( 2 , -5 ,-5)

v1 = x/||x|| = (2, 4, 4)/sqrt36 = ( 1/3, 2/3 , 2/3) ( normalised)

v2 = y - <y ,v1>/<v1, v1>(v1) = (-1,1,4) - (-1/3+2/3+8/3)/(1/9 +4/9+4/9)(1/3, 2/3 , 2/3)

= (-1, 1,4) - (3)/1(1/3, 2/3 , 2/3)

= ( - 1, 1 , 4) - (1 , 2 , 2)

=( -2 .-1, 2)

= ( -2/3 , -1/3 , 2/3) ( normalised)

v3 = z - <z, v1>/<v1, v1>(v1) - <z,v2>/<v2, v2>(v2)

=( 2, -5 , -5) - ( 2/3-10/3-10/3)/(1)( 1/3, 2/3 , 2/3) - 9/9( -2 .-1, 2)

=(2 , -5 , -5) - (-6)(1/3 , 2/3 . 2/3) - (-2, -1 ,2)

= ( 2/3 , -2/3 , 1/3) ( normalise)