Numworks: 3 x 3 Matrices
The script invthree.py calculates the inverse and determinant of a 3 x 3 matrix.
Matrices:
[[ a1, a2, a3 ]
[ b1, b2, b3 ]
[ c1, c2, c3 ]]
Numworks script invthree.py:
(701 bytes)
from math import *
# 2020-11-12 EWS
print("3x3 Matrix Inverse")
print("[[a1,a2,a3]")
print("[b1,b2,b3]")
print("[c1,c2,c3]]")
a1=float(input('a1: '))
a2=float(input('a2: '))
a3=float(input('a3: '))
b1=float(input('b1: '))
b2=float(input('b2: '))
b3=float(input('b3: '))
c1=float(input('c1: '))
c2=float(input('c2: '))
c3=float(input('c3: '))
# determinant
d=a1*(b2*c3-b3*c2)-a2*(b1*c3-b3*c1)+a3*(b1*c2-b2*c1)
# inverse
d1=(b2*c3-c2*b3)/d
d2=-(a2*c3-c2*a3)/d
d3=(a2*b3-a3*b2)/d
e1=-(b1*c3-c1*b3)/d
e2=(a1*c3-c1*a3)/d
e3=-(a1*b3-a3*b1)/d
f1=(b1*c2-b2*c1)/d
f2=-(a1*c2-a2*c1)/d
f3=(a1*b2-a2*b1)/d
print("det=")
print(d)
print("inv=")
print([d1,d2,d3])
print([e1,e2,e3])
print([f1,f2,f3])
Numworks page: https://workshop.numworks.com/python/ews31415/invthree
Example:
[[ -5.4, 3.3, -1.7 ], [ 0.6, 8.3, 5.3 ] [ 5.5, 5.4, 1.9 ]]
returns
[ -0.05493..., -0.06604..., 0.13508... ]
[ 0.11974... , -0.00389..., 0.11798... ]
[ -0.18130..., 0.20224..., -0.20006... ]
Source:
wikiHow Staff "How to Find the Inverse of a 3x3 Matrix" WikiHow. Last Updated November 5, 2020. https://www.wikihow.com/Find-the-Inverse-of-a-3x3-Matrix Retrieved November 12, 2020.
Eddie
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