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Problem: qr decomposition [[1,-1,4],[1,4,-2],[1,4,2],[1,-1,0]] [ Calculator, Method and examples ]

Solution:
Your problem -> qr decomposition [[1,-1,4],[1,4,-2],[1,4,2],[1,-1,0]]

Here A =
 1 -1 4 1 4 -2 1 4 2 1 -1 0

q_1'=a_1 =
 1 1 1 1
=
 1 1 1 1

r_(11)=||q_1'||=sqrt(1^2+1^2+1^2+1^2)=sqrt(4)=2

q_1 = 1/(||q_1'||) * q_1' = 1/2 *
 1 1 1 1
=
 1/2 1/2 1/2 1/2

r_(12)=q_1^T * a_2 =
 [ 1/2 1/2 1/2 1/2 ]
xx
 -1 4 4 -1
=3

q_2'=a_2-r_(12) * q_1 =
 -1 4 4 -1
-3
 1/2 1/2 1/2 1/2
=
 -5/2 5/2 5/2 -5/2

r_(22)=||q_2'||=sqrt((-2.5)^2+2.5^2+2.5^2+(-2.5)^2)=sqrt(25)=5

q_2 = 1/(||q_2'||) * q_2' = 1/5 *
 -5/2 5/2 5/2 -5/2
=
 -1/2 1/2 1/2 -1/2

r_(13)=q_1^T * a_3 =
 [ 1/2 1/2 1/2 1/2 ]
xx
 4 -2 2 0
=2

r_(23)=q_2^T * a_3 =
 [ -1/2 1/2 1/2 -1/2 ]
xx
 4 -2 2 0
=-2

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