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Álgebra lineal Ejemplos
Paso 1
Paso 1.1
Two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. In this case, the first matrix is and the second matrix is .
Paso 1.2
Multiplica cada fila en la primera matriz por cada columna en la segunda matriz.
Paso 1.3
Simplifica cada elemento de la matriz mediante la multiplicación de todas las expresiones.
Paso 2
Paso 2.1
Choose the row or column with the most elements. If there are no elements choose any row or column. Multiply every element in row by its cofactor and add.
Paso 2.1.1
Consider the corresponding sign chart.
Paso 2.1.2
The cofactor is the minor with the sign changed if the indices match a position on the sign chart.
Paso 2.1.3
The minor for is the determinant with row and column deleted.
Paso 2.1.4
Multiply element by its cofactor.
Paso 2.1.5
The minor for is the determinant with row and column deleted.
Paso 2.1.6
Multiply element by its cofactor.
Paso 2.1.7
The minor for is the determinant with row and column deleted.
Paso 2.1.8
Multiply element by its cofactor.
Paso 2.1.9
Add the terms together.
Paso 2.2
Multiplica por .
Paso 2.3
Evalúa .
Paso 2.3.1
El determinante de una matriz puede obtenerse usando la fórmula .
Paso 2.3.2
Simplifica cada término.
Paso 2.3.2.1
Mueve a la izquierda de .
Paso 2.3.2.2
Reescribe como .
Paso 2.3.2.3
Multiplica .
Paso 2.3.2.3.1
Multiplica por .
Paso 2.3.2.3.2
Multiplica por .
Paso 2.4
Evalúa .
Paso 2.4.1
El determinante de una matriz puede obtenerse usando la fórmula .
Paso 2.4.2
Simplifica cada término.
Paso 2.4.2.1
Mueve a la izquierda de .
Paso 2.4.2.2
Reescribe como .
Paso 2.4.2.3
Multiplica .
Paso 2.4.2.3.1
Multiplica por .
Paso 2.4.2.3.2
Multiplica por .
Paso 2.5
Simplifica el determinante.
Paso 2.5.1
Suma y .
Paso 2.5.2
Simplifica cada término.
Paso 2.5.2.1
Aplica la propiedad distributiva.
Paso 2.5.2.2
Reescribe con la propiedad conmutativa de la multiplicación.
Paso 2.5.2.3
Multiplica por .
Paso 2.5.2.4
Multiplica por sumando los exponentes.
Paso 2.5.2.4.1
Mueve .
Paso 2.5.2.4.2
Multiplica por .
Paso 2.5.2.5
Aplica la propiedad distributiva.
Paso 2.5.2.6
Reescribe con la propiedad conmutativa de la multiplicación.
Paso 2.5.2.7
Multiplica por .
Paso 2.5.2.8
Simplifica cada término.
Paso 2.5.2.8.1
Multiplica por sumando los exponentes.
Paso 2.5.2.8.1.1
Mueve .
Paso 2.5.2.8.1.2
Multiplica por .
Paso 2.5.2.8.2
Multiplica por .
Paso 2.5.3
Suma y .
Paso 2.5.4
Resta de .
Paso 3
Since the determinant is non-zero, the inverse exists.
Paso 4
Set up a matrix where the left half is the original matrix and the right half is its identity matrix.
Paso 5
Paso 5.1
Multiply each element of by to make the entry at a .
Paso 5.1.1
Multiply each element of by to make the entry at a .
Paso 5.1.2
Simplifica .
Paso 5.2
Perform the row operation to make the entry at a .
Paso 5.2.1
Perform the row operation to make the entry at a .
Paso 5.2.2
Simplifica .
Paso 5.3
Multiply each element of by to make the entry at a .
Paso 5.3.1
Multiply each element of by to make the entry at a .
Paso 5.3.2
Simplifica .
Paso 5.4
Perform the row operation to make the entry at a .
Paso 5.4.1
Perform the row operation to make the entry at a .
Paso 5.4.2
Simplifica .
Paso 5.5
Multiply each element of by to make the entry at a .
Paso 5.5.1
Multiply each element of by to make the entry at a .
Paso 5.5.2
Simplifica .
Paso 5.6
Perform the row operation to make the entry at a .
Paso 5.6.1
Perform the row operation to make the entry at a .
Paso 5.6.2
Simplifica .
Paso 5.7
Perform the row operation to make the entry at a .
Paso 5.7.1
Perform the row operation to make the entry at a .
Paso 5.7.2
Simplifica .
Paso 5.8
Perform the row operation to make the entry at a .
Paso 5.8.1
Perform the row operation to make the entry at a .
Paso 5.8.2
Simplifica .
Paso 6
The right half of the reduced row echelon form is the inverse.