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6: Mapas lineales

Última actualización

30 oct 2022
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- 5.E: Ejercicios para el Capítulo 5
- 6.1: Deﬁnición y propiedades elementales

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Como se discute en el Capítulo 1, uno de los principales objetivos del Álgebra Lineal es la caracterización de soluciones a un sistema de $m$ linear equations in $n$ unknowns $x_1, \ldots, x_n$ ,

\ [\ begin {ecuación*}
\ izquierda.
\ begin {array} {rl}
a_ {11} x_1 +\ cdots + a_ {1n} x_n &= b_1\\
\ vdots\ qquad\ vdots\ qquad &\ quad\ vdots\\
a_ {m1} x_1 +\ cdots + a_ {mn} x_n &= b_m
\ end {array}
\ right\},
\ end {ecuación*}\]

where each of the coefficients $a_{ij}$ and $b_i$ is in $\mathbb{F}$ . Linear maps and their properties give us insight into the characteristics of solutions to linear systems.

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