Operaciones con matrices

SUMA Y RESTA DE MATRICES

LA SUMA, A + B, dos matrices A y C del mismo tamaño se obtiene sumando los elementos de ambas matrices. Para la RESTA, A - B, se restan les elementos correspondientes. Las matrices de distintos tamaños no se pueden sumar ni restar.

• Ejemplo

 A= $\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$ , B= $\left[\begin{array}{cc}{b}_{11}& b_{12}\\ b_{21}& b_{22}\end{array}\right]$    A + B =  $\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$ + $\left[\begin{array}{cc}{b}_{11}& b_{12}\\ b_{21}& b_{22}\end{array}\right]$ = $\left[\begin{array}{cc}{a}_{11}+b_{11}& a_{12}+b_{12}\\ a_{21}+b_{21}& a_{22}+b_{22}\end{array}\right]$                                                                                                                                  .
      A = $\left[\begin{array}{cc}1& 3\\ 5& 7\end{array}\right]$  ,   B   =  $\left[\begin{array}{cc}2& 4\\ 6& 8\end{array}\right]$

La suma se hace componente a componente.

A      +     B    =   $\left[\begin{array}{cc}1& 3\\ 5& 7\end{array}\right]+\left[\begin{array}{cc}2& 4\\ 6& 8\end{array}\right]=\left[\begin{array}{cc}1+2& 3+4\\ 5+6& 7+8\end{array}\right]$ = $\left[\begin{array}{cc}3& 7\\ 11& 15\end{array}\right]$

algo mas general se puede describir como:

A = $\left[\begin{array}{ccc}{a}_{11}& \cdots & a_{1n}\\ ⋮& \ddots & ⋮\\ a_{1n}& \cdots & a_{nn}\end{array}\right]$ , B = $\left[\begin{array}{ccc}{b}_{11}& \cdots & b_{1n}\\ ⋮& \ddots & ⋮\\ b_{1n}& \cdots & b_{nn}\end{array}\right]$

A + B = $\left[\begin{array}{ccc}{a}_{11}+b_{11}& \cdots & a_{1n}+b_{1n}\\ ⋮& \ddots & ⋮\\ a_{1n}+b_{1n}& \cdots & a_{nn}+b_{nn}\end{array}\right]$

Ejemplo 2

A - B = $\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]$ - $\left[\begin{array}{cc}{b}_{11}& b_{12}\\ b_{21}& b_{22}\end{array}\right]$ = $\left[\begin{array}{cc}{a}_{11}-b_{11}& a_{12}-b_{12}\\ a_{21}-b_{21}& a_{22}-b_{22}\end{array}\right]$ .

La resta se hace componente a componente.

A      -     B    =   $\left[\begin{array}{cc}1& 3\\ 5& 7\end{array}\right]-\left[\begin{array}{cc}2& 4\\ 6& 8\end{array}\right]=\left[\begin{array}{cc}1-2& 3-4\\ 5-6& 7-8\end{array}\right]$ = $\left[\begin{array}{cc}-1& -1\\ -1& -1\end{array}\right]$

algo mas general se puede describir como:

A = $\left[\begin{array}{ccc}{a}_{11}& \cdots & a_{1n}\\ ⋮& \ddots & ⋮\\ a_{1n}& \cdots & a_{nn}\end{array}\right]$ , B = $\left[\begin{array}{ccc}{b}_{11}& \cdots & b_{1n}\\ ⋮& \ddots & ⋮\\ b_{1n}& \cdots & b_{nn}\end{array}\right]$

A - B = $\left[\begin{array}{ccc}{a}_{11}-b_{11}& \cdots & a_{1n}-b_{1n}\\ ⋮& \ddots & ⋮\\ a_{1n}-b_{1n}& \cdots & a_{nn}-b_{nn}\end{array}\right]$