# How do you find the determinant by cofactor expansion?

## How do you find the determinant by cofactor expansion?

To compute the cofactor expansion of a 3×3 matrix, you have to:

1. Choose a row/column of your matrix.
2. For each coefficient in your row/column, compute the respective 2×2 cofactor.
3. Multiply the coefficient by its cofactor.
4. Add the three numbers obtained in steps 2 & 3.
5. This is your determinant!

## How is a determinant of order 3 expanded?

Determinant of a matrix of order three can be determined by expressing it in terms of second order determinants. This is known as expansion of a determinant along a row or a column. There are 6 ways of expanding a determinant of order 3 corresponding to each of 3 rows (R1, R2 and R3) and 3 columns (C1, C2 and C3).

How many ways can you expand a 3 by 3 determinant?

4.1.3 Determinant of a matrix of order three There are six ways of expanding a determinant of order 3 corresponding to each of three rows (R1, R2 and R3) and three columns (C1, C2 and C3) and each way gives the same value.

### How to find determinant 5×5?

Determinant 5×5

• Enter the coefficients
• Calculating the determinant value with Laplace expansion. You can select the row or column to be used for expansion.
• Calculation with the Gaussian Algorithm. If leading coefficients zero then should be columns or rows are swapped accordingly so that a divison by the leading coefficient is possible.
• ### How to solve a 2×3 matrix?

To solve a 2×3 matrix, for example, you use elementary row operations to transform the matrix into a triangular one. Elementary operations include: swapping two rows. multiplying a row by a number different from zero. multiplying one row and then adding to another row. Multiply the second row by a non-zero number.

How do you find determinant?

Here are the steps to go through to find the determinant. Pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row. Multiply every element in that row or column by its cofactor and add. The result is the determinant.

## How do you find the inverse of a matrix?

Using a Calculator to Find the Inverse Matrix Select a calculator with matrix capabilities. Enter your matrix into the calculator. Select the Edit submenu. Select a name for your matrix. Enter the dimensions of your matrix. Enter each element of the matrix. Quit the Matrix function. Use the inverse key to find the inverse matrix.