Write your code: Matrix Determinant

Write functions that return the determinant of square matrix of orders (\(2\times2\)), (\(3\times3\)), and (\(n\times n\)).

Rules

1. Function returns a integer.

2. You must not use any external function to calculate the determinant.

Useful Links

• Determinant

• Minor of Matrix

• Cofactor Expansion

Function Definition

import numpy as np

def get_minor_ij(A, i, j):
    M = np.delete(A, i-1, axis=0) # remove a row (axis=0)
    M = np.delete(M, j-1, axis=1) # remove a column (axis=1)

    return M

Order 2

A = np.array([[ 2, 5],
              [ 1, -3]]
            )

# numpy determinant function:
round(np.linalg.det(A))

-11

def get_determinant_2(A):
  
  # write your function here

get_determinant_2(A)

  File "/tmp/ipykernel_1856/682844987.py", line 5
    get_determinant_2(A)
                    ^
IndentationError: expected an indented block

Order 3

A = np.array([[ 9, 12, 18],
              [ 2, -2,  5],
              [11,-17, 19]]
            )

# numpy determinant function:
round(np.linalg.det(A))

def get_determinant_3(A):

    # write your function here

get_determinant_3(A)

Larger Orders: recursive solution

A = np.array([[5, 2, 1, 4, 6],
              [9, 4, 2, 5, 2],
              [11, 5, 7, 3, 9],
              [5, 6, 6, 7, 2],
              [7, 5, 9, 3, 3]])

# numpy determinant function:
round(np.linalg.det(A))

def get_determinant_n(A):

    # write your function here

get_determinant_n(A)