Álgebra lineal Ejemplos

Hallar la preimagen x([[a],[b],[d]])=[[5a+3b-2d],[0a+4b-d]] , [[14],[2]]
,
Paso 1
Write as an augmented matrix for .
Paso 2
Write as a linear system of equations.
Paso 3
Resuelve el sistema de ecuaciones.
Toca para ver más pasos...
Paso 3.1
Move variables to the left and constant terms to the right.
Toca para ver más pasos...
Paso 3.1.1
Reordena los factores en .
Paso 3.1.2
Mueve .
Paso 3.2
Write the system as a matrix.
Paso 3.3
Obtén la forma escalonada reducida por filas.
Toca para ver más pasos...
Paso 3.3.1
Multiply each element of by to make the entry at a .
Toca para ver más pasos...
Paso 3.3.1.1
Multiply each element of by to make the entry at a .
Paso 3.3.1.2
Simplifica .
Paso 3.3.2
Perform the row operation to make the entry at a .
Toca para ver más pasos...
Paso 3.3.2.1
Perform the row operation to make the entry at a .
Paso 3.3.2.2
Simplifica .
Paso 3.3.3
Multiply each element of by to make the entry at a .
Toca para ver más pasos...
Paso 3.3.3.1
Multiply each element of by to make the entry at a .
Paso 3.3.3.2
Simplifica .
Paso 3.3.4
Perform the row operation to make the entry at a .
Toca para ver más pasos...
Paso 3.3.4.1
Perform the row operation to make the entry at a .
Paso 3.3.4.2
Simplifica .
Paso 3.4
Use the result matrix to declare the final solution to the system of equations.
Paso 3.5
Write a solution vector by solving in terms of the free variables in each row.
Paso 3.6
Write the solution as a linear combination of vectors.
Paso 3.7
Write as a solution set.