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= ${\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{bmatrix}}$ , B= ${\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}$    A + B =  ${\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{bmatrix}}$ + ${\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}$ = ${\begin{bmatrix}a_{11}+b_{11}&a_{12}+b_{12}\\a_{21}+b_{21}&a_{22}+b_{22}\end{bmatrix}}$                                                                                                                                  .
      A = ${\begin{bmatrix}1&3\\5&7\end{bmatrix}}$  ,   B   =  ${\begin{bmatrix}2&4\\6&8\end{bmatrix}}$

La suma se hace componente a componente.

A      +     B    =   ${\begin{bmatrix}1&3\\5&7\end{bmatrix}}+{\begin{bmatrix}2&4\\6&8\end{bmatrix}}={\begin{bmatrix}1+2&3+4\\5+6&7+8\end{bmatrix}}$ = ${\begin{bmatrix}3&7\\11&15\end{bmatrix}}$

algo mas general se puede describir como:

A = ${\begin{bmatrix}a_{11}&\cdots &a_{1n}\\\vdots &\ddots &\vdots \\a_{1n}&\cdots &a_{nn}\end{bmatrix}}$ , B = ${\begin{bmatrix}b_{11}&\cdots &b_{1n}\\\vdots &\ddots &\vdots \\b_{1n}&\cdots &b_{nn}\end{bmatrix}}$

A + B = ${\begin{bmatrix}a_{11}+b_{11}&\cdots &a_{1n}+b_{1n}\\\vdots &\ddots &\vdots \\a_{1n}+b_{1n}&\cdots &a_{nn}+b_{nn}\end{bmatrix}}$

Ejemplo 2

A - B = ${\begin{bmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{bmatrix}}$ - ${\begin{bmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{bmatrix}}$ = ${\begin{bmatrix}a_{11}-b_{11}&a_{12}-b_{12}\\a_{21}-b_{21}&a_{22}-b_{22}\end{bmatrix}}$ .

La resta se hace componente a componente.

A      -     B    =   ${\begin{bmatrix}1&3\\5&7\end{bmatrix}}-{\begin{bmatrix}2&4\\6&8\end{bmatrix}}={\begin{bmatrix}1-2&3-4\\5-6&7-8\end{bmatrix}}$ = ${\begin{bmatrix}-1&-1\\-1&-1\end{bmatrix}}$

algo mas general se puede describir como:

A = ${\begin{bmatrix}a_{11}&\cdots &a_{1n}\\\vdots &\ddots &\vdots \\a_{1n}&\cdots &a_{nn}\end{bmatrix}}$ , B = ${\begin{bmatrix}b_{11}&\cdots &b_{1n}\\\vdots &\ddots &\vdots \\b_{1n}&\cdots &b_{nn}\end{bmatrix}}$

A - B = ${\begin{bmatrix}a_{11}-b_{11}&\cdots &a_{1n}-b_{1n}\\\vdots &\ddots &\vdots \\a_{1n}-b_{1n}&\cdots &a_{nn}-b_{nn}\end{bmatrix}}$