Adjunta de una matriz 2x2 | Álgebra lineal

Name: Adjunta de una matriz 2x2 | Álgebra lineal
Uploaded: 2018-03-30T05:50:37.000Z
Duration: 6 min 27 s
Description: En este video se explicará detalladamente cómo calcular la matriz adjunta de una matriz de dimensiones 2x2, donde la matriz adjunta es la traspuesta de la matriz de cofactores.

How to Calculate the Adjoint Matrix of a 2x2 Matrix

Introduction to Adjoint Matrices

The video introduces the concept of calculating the adjoint matrix for a 2x2 matrix with elements 3, -5, and 4.

It emphasizes that the adjoint of a matrix is equal to its transpose of the cofactor matrix.

Steps to Calculate Cofactor Matrix

The first step involves determining the cofactor for the element in position (1,1), which is 3. By removing its row and column, we find that its cofactor is 4.

For the second element (1,2), which is -5, after eliminating its row and column, we get -1 as its cofactor since it’s an odd position (sign changes).

The process continues with calculating cofactors for all elements:

For -5 at (2,1), we find +1 as its cofactor due to an odd position.

For 4 at (2,2), we determine that it remains +3 because it's in an even position.

Forming the Cofactor Matrix

After calculating all cofactors, we compile them into a cofactor matrix:

| 4 5 |

| -1 3 |

Transposing to Find Adjoint Matrix

To obtain the adjoint matrix, we transpose the cofactor matrix by converting rows into columns:

| 4 -1 |

| 5 3 |

Observations on Adjoint Matrix Structure

The final adjoint matrix shows similarities with the original matrix; specifically:

Diagonal elements are inverted from original positions.

Video description

En este video se explicará detalladamente cómo calcular la matriz adjunta de una matriz de dimensiones 2x2, donde la matriz adjunta es la traspuesta de la matriz de cofactores.