Matrices

Las matrices son un conjunto de vectores fila y columna.

\[B=\begin{pmatrix}-1 & 2 & 3 \\ 4&5&-6 \\-7&-8&-9 \end{pmatrix}\]

B=matrix(c(-1,2,3,4,5,-6,-7,-8,-9),nrow=3,ncol=3,byrow=TRUE)
B

##      [,1] [,2] [,3]
## [1,]   -1    2    3
## [2,]    4    5   -6
## [3,]   -7   -8   -9

Suma de matrices

La suma de matrices es componente a componente

\[B=\begin{pmatrix}-1 & 2 & 3 \\ 4&5&-6 \\-7&-8&-9 \end{pmatrix} \ C=\begin{pmatrix}1 & 0 & 3 \\ 4&0&6 \\9&10&11 \end{pmatrix}\]

B=matrix(c(-1,2,3,4,5,-6,-7,-8,-9),nrow=3,ncol=3,byrow=TRUE)
B

##      [,1] [,2] [,3]
## [1,]   -1    2    3
## [2,]    4    5   -6
## [3,]   -7   -8   -9

C=matrix(c(1,0,3,4,0,6,9,10,11),3,3,byrow=TRUE)
C

##      [,1] [,2] [,3]
## [1,]    1    0    3
## [2,]    4    0    6
## [3,]    9   10   11

C+B

##      [,1] [,2] [,3]
## [1,]    0    2    6
## [2,]    8    5    0
## [3,]    2    2    2

Una transpuesta es cambiar filas por columnas \[A^T\]

t(B)

##      [,1] [,2] [,3]
## [1,]   -1    4   -7
## [2,]    2    5   -8
## [3,]    3   -6   -9

Hallar el valor de las variales de un sistema de ecuaciones lineal

\[\begin{cases} 2x+y=5\\ x+3y=7 \end{cases}\]

A=matrix(c(2,1,1,3),2,2,byrow=TRUE)
b=c(5,7)
solucion=solve(A,b)
solucion

## [1] 1.6 1.8