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{equation} \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} \end{equation}

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{equation} \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} \end{equation}

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

Calcula:

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