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Matrices

Suma y resta de matrices

Para sumar matrices, se suman cada uno de los términos de la matriz.

$\fs2\left[\begin{array}a_{11}&a_{12}&\cdots&a_{1m}\\a_{21}&a_{22}&\cdots&a_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}&a_{n2}&\cdots&a_{nm}\end{array}\right]+\left[\begin{array}b_{11}&b_{12}&\cdots&b_{1m}\\b_{21}&b_{22}&\cdots&b_{2m}\\\vdots&\vdots&\ddots&\vdots\\b_{n1}&b_{n2}&\cdots&b_{nm}\end{array}\right]=\left[\begin{array}a_{11}+b_{11}&a_{12}+b_{12}&\cdots&a_{1m}+b_{1m}\\a_{21}+b_{21}&a_{22}+b_{22}&\cdots&a_{2m}+b_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}+b_{n1}&a_{n2}+b_{n2}&\cdots&a_{nm}+b_{nm}\end{array}\right]$

$$\begin{pmatrix} 2&-1&2\\0&-3&1\\4&0&1\end{pmatrix} +\begin{pmatrix}3&1&2\\0&2&-7\\0&0&-2\end{pmatrix} = \begin{pmatrix}5&0&4\\0&-1&-6\\4&0&-1\end{pmatrix}$$

Para restar matrices, se restan cada uno de los términos de la matriz.
$\fs2\left[\begin{array}a_{11}&a_{12}&\cdots&a_{1m}\\a_{21}&a_{22}&\cdots&a_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}&a_{n2}&\cdots&a_{nm}\end{array}\right]-\left[\begin{array}b_{11}&b_{12}&\cdots&b_{1m}\\b_{21}&b_{22}&\cdots&b_{2m}\\\vdots&\vdots&\ddots&\vdots\\b_{n1}&b_{n2}&\cdots&b_{nm}\end{array}\right]=\left[\begin{array}a_{11}-b_{11}&a_{12}-b_{12}&\cdots&a_{1m}-b_{1m}\\a_{21}-b_{21}&a_{22}-b_{22}&\cdots&a_{2m}-b_{2m}\\\vdots&\vdots&\ddots&\vdots\\a_{n1}-b_{n1}&a_{n2}-b_{n2}&\cdots&a_{nm}-b_{nm}\end{array}\right]$

$$\begin{pmatrix} 2&-1&2\\0&-3&1\\4&0&1\end{pmatrix} -\begin{pmatrix}3&1&2\\0&2&-7\\0&0&-2\end{pmatrix} = \begin{pmatrix}-1&-2&0\\0&-5&8\\4&0&3\end{pmatrix}$$

No olvides que para poder sumar o restar matrices, deben tener la misma dimensión.

Calcula:

 $$\begin{pmatrix}2&1&4\\-2&-3&-3\end{pmatrix}-\begin{pmatrix}-4&5&0\\-2&-1&-3\end{pmatrix}=$$