Enter the matrix A, row and column indices i and j, and the element a_ij into the calculator to determine the determinant of a matrix using cofactors.

## Cofactor Determinant Formula

The following formula is used to calculate the determinant of a matrix using cofactors.

Det(A) = Σ (-1)^{(i+j)} * a_ij * Det(M_ij)

Variables:

• Det(A) is the determinant of matrix Ai and j are the row and column indices of the element a_ij in matrix Aa_ij is an element in matrix ADet(M_ij) is the determinant of the sub-matrix that remains after removing the i-th row and j-th column from matrix A

To calculate the determinant using cofactors, for each element a_ij in the matrix, calculate the determinant of the sub-matrix that remains after removing the i-th row and j-th column. Multiply this by the element a_ij and by (-1) raised to the power of (i+j). Sum all these values to get the determinant of the matrix.

## What is a Cofactor Determinant?

A cofactor determinant is a mathematical concept used in the calculation of the determinant of a square matrix. It involves the use of cofactors, which are sub-matrices derived from the original matrix by removing one row and one column. The determinant of a matrix is calculated by multiplying each element of a row or column by the determinant of its cofactor and then summing these products, with alternating signs. This process can be recursively applied to calculate the determinants of larger matrices.

## How to Calculate Cofactor Determinant?

The following steps outline how to calculate the Cofactor Determinant using the given formula:

1. First, identify the matrix A.
2. Next, determine the value of i and j for each element a_ij in matrix A.
3. For each element a_ij, calculate (-1)^(i+j) * a_ij * Det(M_ij).
4. Sum up all the calculated values from step 3.
5. The final result is the Cofactor Determinant of matrix A.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Matrix A:

| 2 3 1 |

| 4 0 -2 |

| 1 -1 3 |

Calculate the Cofactor Determinant of matrix A.