5_2_OH.ipynb

Kernel: SageMath (stable)

A = matrix([
        [57,73,81],
        [93,101,113],
        [29,34,38]
    ])
print(A)
print(A.inverse())

[ 57  73  81]
[ 93 101 113]
[ 29  34  38]
[    1/29     5/29   -17/29]
[ 257/116  183/116  -273/29]
[-233/116 -179/116   258/29]

Ainv = A.inverse(); Ainv

[    1/29     5/29   -17/29]
[ 257/116  183/116  -273/29]
[-233/116 -179/116   258/29]

$Ax = b \implies x=A^{-1} b$

b = vector([2262,3218,1071])

A.solve_right(b)

(5, 6, 19)

Ainv * b

(5, 6, 19)

Ab = A.augment(b); Ab

[  57   73   81 2262]
[  93  101  113 3218]
[  29   34   38 1071]

Ab.rref()

[ 1  0  0  5]
[ 0  1  0  6]
[ 0  0  1 19]