Unidad 4. Algebra Lineas, Matrices, Sistemas de Ecuaciones y Determinantes

Matriz

$$\begin{array}{r}A=\left(\begin{array}{ccc}1& 2& 4\\ 7& -1& 3\end{array}\right)\end{array}\text{ Matriz de }2\times 3$$ $$\begin{array}{r}B=\left(\begin{array}{cc}7& -2\\ 1& -5\end{array}\right)\end{array}\text{ Matriz de }2\times 2$$

Operaciones con Matrices

Suma

$$\begin{array}{r}\left(\begin{array}{ccc}5& 2& -3\\ 4& -7& 1\end{array}\right)+\left(\begin{array}{ccc}1& 0& 4\\ -2& 3& 0\end{array}\right)=\left(\begin{array}{ccc}6& 2& -7\\ 2& -4& 1\end{array}\right)\end{array}$$ $$\begin{array}{r}\left(\begin{array}{ccc}1& 2& 4\\ 7& -1& 3\end{array}\right)+\left(\begin{array}{cc}7& -2\\ 1& -5\end{array}\right)\text{ No se pueden sumar }\end{array}$$

Producto

$$\begin{array}{r}-3\times \left(\begin{array}{ccc}5& 2& -3\\ 4& -7& 1\end{array}\right)=\left(\begin{array}{ccc}-15& -6& 9\\ -12& 21& -3\end{array}\right)\end{array}$$

Triangulacion de matrices

$$\begin{array}{r}\left(\begin{array}{ccc}1& 2& 3\\ -1& 0& 5\\ 2& -1& 0\end{array}\right)\begin{array}{l}F{1}^{\prime }=F1\\ F{2}^{\prime }=F2+F1\\ F{3}^{\prime }=2F1-F3\end{array}\Rightarrow \left(\begin{array}{ccc}1& 2& 3\\ 0& 2& 8\\ 0& 5& 6\end{array}\right)\begin{array}{l}F{1}^0=F{1}^{\prime }\\ F{2}^{\prime }=F{2}^{\prime }\\ F{3}^0=5F{2}^{\prime }-2F{3}^{\prime }\end{array}\Rightarrow \left(\begin{array}{ccc}1& 2& 3\\ 0& 2& 8\\ 0& 0& 28\end{array}\right)\end{array}$$