Minor of Matrix

Write a function that returns the Minor of Matrix of a 3x3 Matrix for a given line \((i)\) and column \((j)\)

Rules

1. Function returns a Numpy ndarray of shape=2x2

2. Function should work for all possible \(i,j\) combination

Useful Links

• NumPy Array

• Indexing Methods

  • Specially: ix_()

• NumPy Broadcasting

Minor of Matrix: Definition

Minor of matrix for a particular element in the matrix is defined as the matrix obtained after deleting the row and column of the matrix in which that particular element lies.

- cuemath

Example

For example, consider the following 3x3 square matrix A:

\[\begin{split} A = \begin{bmatrix} 9 & 12 & 18 \\ 2 & -2 & 5 \\ 11 & -17 & 19 \end{bmatrix} \end{split}\]

The Minor of Matrix for the line \(i=1\) and column \(j=1\) is:

\[\begin{split} M_{11} = \begin{bmatrix} -2 & 5 \\ -17 & 19 \end{bmatrix} \end{split}\]

and the Minor of Matrix for the line \(i=2\) and column \(j=3\) is:

\[\begin{split} M_{23} = \begin{bmatrix} 9 & 12 \\ 11 & -17 \end{bmatrix} \end{split}\]

Index Notation

Please note that in Matrix, the index starts with 1. So, first line is index 1. On the other hand, indexing in python starts at zero, so, first line is index 0.

Please remember to add some index “conversion” to ensure that you access the desired index!

Disclaimer

The definition of Minor of Matrix is not exactly the one presented above. The Minor of Matrix is the determinant of the \(M_{ij}\) matrix. But for the sanity of this challenge, let’s stop a step earlier and just get the Matrix \(M_{ij}\) itself.