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inversa de una matriz, obtencion determinante 2 x 2
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notas completas sobre como obtener la inversa de una matriz y tambien como obtener el determinante de una matriz 2x2
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1.5 inversa de una matrizInversa mediante Gauss
Por ejemplo, si A es dimensión 2x2,
Y si es de dimensión 3x3,
Para calcular la matriz inversa de AA, se realizan operaciones elementales fila
para conseguir la forma escalonada reducida de la matriz GG.
Dicho en otras palabras, se realizan operaciones elementales filas hasta conseguir
la matriz identidad en el bloque izquierdo de la matriz GG, es decir,
Al terminar las operaciones, la matriz identidad que había en el lado derecho se ha
transformado en otra matriz BB. Esta matriz BB es precisamente la matriz inversa
de AA.
Construimos la matriz por bloques:
Para obtener la matriz identidad en el bloque izquierdo sólo tenemos que restarle
a la fila 1 cuatro veces la fila 2:
Como ya tenemos la identidad en el bloque izquierdo, la matriz del bloque derecho
es la inversa:
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