Matrices 2. Operaciones by josmar2511

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spanish · @josmar2511 · Apr 27 '19

$4.21

Matrices 2. Operaciones

<div class=text-justify>Hola mis estimados amigos. Bienvenidos, nuevamente, a nuestro rincón matemático, les invito a un nuevo paseo por el mundo de las matrices. En esta nueva oportunidad, les quiero compartir lo referido a las operaciones con matrices. Sin más, comencemos nuestro acostumbrado recorrido.

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<center>![portada.png](https://cdn.steemitimages.com/DQmVD6ZHAUYpPvKC7KZwNsoNcC86DPRyLdfMKQkatcfNZb7/portada.png)</center>
<center>[link](https://cdn.steemitimages.com/DQmVD6ZHAUYpPvKC7KZwNsoNcC86DPRyLdfMKQkatcfNZb7/portada.png)</center>

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<h1>Operaciones con matrices</h1>

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Antes de iniciar, de manera específica, con las operaciones entre matrices, resulta  oportuno señalar lo que tiene que ver con la igualdad de matrices, en este sentido, referimos:

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<center>![matrices iguales.PNG](https://cdn.steemitimages.com/DQmYFR65S3CtnYJ4cYCaR1E14tjgKeJT845Lepb9QJzMQ3k/matrices%20iguales.PNG)</center>

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O sea:   (aij) = (bij) si y sólo si aij = bij  para cada i y para cada j.



   


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Ahora si, vayamos a las operaciones con matrices.

<h1>1.- Suma de matrices</h1>

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Sean  (aij) y (bij) dos matrices del mismo orden mxn. La matriz suma se obtiene, genéricamente, como se indica:



 Sumamos:         (aij) + (bij)= (aij +  bij)

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<center>![Matrices Suma.PNG](https://cdn.steemitimages.com/DQmS2UWLG9cr9cZWsoGxhNhQzQdDyjd2sEpsPLTZjXsYnAd/Matrices%20Suma.PNG)</center>

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   <center>![ejemplo.PNG](https://cdn.steemitimages.com/DQmcD9UqjQ9UAamzwbDwwL5XyCZRy5gjZzRy5LXeNAhWyyk/ejemplo.PNG)</center>


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<center>![suma de matrices.PNG](https://cdn.steemitimages.com/DQmWBWspTJ7HH8QdW3cD4cTUZWyWNL2c9HJdnKvatScTg7d/suma%20de%20matrices.PNG)</center>


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<h1>2.- Multiplicación de una matriz por un número</h1>

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Sean  (aij) una matriz de orden mxn y r un número real. Definimos el  producto de r por la matriz (aij) como se escribe a continuación:

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Nótese :                                  r . (aij) = (r.aij)

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<center>![matrices multiplicacion.PNG](https://cdn.steemitimages.com/DQmdGqpbMfsFVGxh1ApyCMvRpW6TF8jedzFfyMzQAJXKvCD/matrices%20multiplicacion.PNG)</center>

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<center>![ejemplo.PNG](https://cdn.steemitimages.com/DQmcD9UqjQ9UAamzwbDwwL5XyCZRy5gjZzRy5LXeNAhWyyk/ejemplo.PNG)</center>

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<center>![numero por matriz.PNG](https://cdn.steemitimages.com/DQmXewwo1HPG1tusisJzybLof4mL2CecxGUv3eskTbzUHt8/numero%20por%20matriz.PNG)</center>

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<h1>3.- Multiplicación de matrices</h1>

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Inicialmente, debemos reconocer que no todas las matrices pueden multiplicarse. Es necesario que la matriz que cumple la función de ser el primer factor sea de orden  mxn y la segunda matriz, segundo factor da la multiplicación, sea de orden nxp; dicho de otra manera, sólo se pueden multiplicar dos matrices cuando el número de columnas de la primera matriz que multiplica coincide con el número de filas de la segunda matriz. Así, la matriz resultante sera de tamaño , u orden, mxp.

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<center>![multiplicacion de matrices.PNG](https://cdn.steemitimages.com/DQmPP4LZTWncEsYLQZARaDRj3ntRXhZTTyEH3VQq1W5W2r7/multiplicacion%20de%20matrices.PNG)</center>

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<center>![ejemplo.PNG](https://cdn.steemitimages.com/DQmcD9UqjQ9UAamzwbDwwL5XyCZRy5gjZzRy5LXeNAhWyyk/ejemplo.PNG)</center>

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Supóngase que, los consumos anuales de 4 familias X,Y, Z y T en fruta, pescado y queso vienen dados por la matriz A. Los precios de esos mismos productos en los años 1993 y 1994 venían dados por la matriz B.

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<center>![primer factor.PNG](https://cdn.steemitimages.com/DQmdcCDaPsBzNa2gzmyEYHrHvLqdWLcHuDvC7VbdpYL4MYH/primer%20factor.PNG)</center>

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<center>![segundo factor.PNG](https://cdn.steemitimages.com/DQmUKWv3Xq1aGV7HkTZoFL5cpT7gTwaFaExQHgLvTYhwi9R/segundo%20factor.PNG)</center>

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La matriz A.B nos dará el gasto en frutas, pescado y queso de cada familia por año, así:

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<center>![resultado practico.PNG](https://cdn.steemitimages.com/DQmcoAHSf7QtCccnDUvCNXj82tRZbeRoCbbxAdV7yUdja8V/resultado%20practico.PNG)</center>

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Así, por ejemplo, podemos afirmar que la familia Z gastó 73840 bolívares en fruta, pescado y queso en 1993. Mientras que la familia X, en 1994, gastaba 154590 en los mismo 3 alimentos, antes referidos.

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Veamos, ya para concluir, a modo de afianzar el cálculo del resultado, cómo se obtuvo, por ejemplo, el  elemento    c11= 154590 de la matriz gasto.</div>

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<center>![Prueba.PNG](https://cdn.steemitimages.com/DQmRQgdVAqspK39KDjPKgbit34TesvgWJLc1gAcCpRJvCTW/Prueba.PNG)</center>

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> ***Bueno amigos, si me han acompañado hasta acá, muchas gracias. Nos vemos en próximo encuentro donde la matemática y steemit, serán, nuevamente, protagonistas. Saludos!!***

👍 blocktrades, cervantes, wackou, delegate.lafona, pgarcgo, heiditravels, gargon, edu-venezuela, minnowsupport, jgcastrillo19, wartrapa, titin, ramonycajal, theclub, electrodo, supu, eforucom, mdcomes, hijosdelhombre, teo, dulcinea, jkj, maticpecovnik, dcardozo25, josmar2511, noticias, spanishchef, maastro, solmar, mariacherries, velazquezboy, mys, albagargon, soredesi, trans-juanmi, xyzashu, reimerlin, sportsven, imperfect-one, kaux, cindycam, simonmaz, deisip67, coquiunlimited, gmart, reinaseq, vensport, purapapita, perniachiquito, vensports, julian.alejandro, fidel-castro, patris, fullnews, edwinbasu, magoia, fredhm, arausi, newsport, fotoven, joso, alex-hm, desikaamukkahani, kilianmiguel, and 92 others

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@edu-venezuela · May 3 '19

![](https://cdn.steemitimages.com/DQmP84f1hqQC2iss6hpzJsB5d5crYdah9UTMa2ZFnLVC56k/image.png)

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@minnowsupport · Apr 28 '19

<p>Congratulations!  This post has been upvoted from the communal account, @minnowsupport, by josmar2511 from the Minnow Support Project. It's a witness project run by aggroed, ausbitbank, teamsteem, someguy123, neoxian, followbtcnews, and netuoso. The goal is to help Steemit grow by supporting Minnows.  Please find us at the <a href="https://discord.gg/HYj4yvw"> Peace, Abundance, and Liberty Network (PALnet) Discord Channel</a>.  It's a completely public and open space to all members of the Steemit community who voluntarily choose to be there.</p> <p>If you would like to delegate to the Minnow Support Project you can do so by clicking on the following links: <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=102530.639667%20VESTS">50SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=205303.639667%20VESTS">100SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=514303.639667%20VESTS">250SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=1025303.639667%20VESTS">500SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=2053030.639667%20VESTS">1000SP</a>, <a href="https://v2.steemconnect.com/sign/delegateVestingShares?delegator=&amp;delegatee=minnowsupport&amp;vesting_shares=10253030.639667%20VESTS">5000SP</a>. <br><strong>Be sure to leave at least 50SP undelegated on your account.</strong></p>

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@ramonycajal · Apr 28 '19

![CURADORES-01.gif](https://cdn.steemitimages.com/DQmdARgRdaxHcoZjoWaV4p17QyaAteKSPLXRS11y2b3MvdG/CURADORES-01.gif)

👍 wilsonlozano

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@josmar2511 · Apr 28 '19

Muchas gracias al equipo de @ramonycajal y la comunidad de @cervantes por tan valioso apoyo. Un abrazo a todos!!

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`total_payout_value`	0.000 HBD
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`pending_payout_value`	0.000 HBD
`promoted`	0.000 HBD
`body_length`	112
`author_reputation`	2,550,985,495,114
`root_title`	"Matrices 2. Operaciones"
`beneficiaries`	`[]`
`max_accepted_payout`	1,000,000.000 HBD
`percent_hbd`	10,000
`post_id`	83,884,985
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@theclub · Apr 27 '19

![](https://cdn.steemitimages.com/DQmPm3T8AegxZTkz5vF26BrhxXSkNxZxXu9WPFJaQkKJxez/imagen.png)

properties (22)

`author`	theclub
`permlink`	re-josmar2511-matrices-2-operaciones-20190427t205447475z
`category`	spanish
`json_metadata`	{"tags":["spanish"],"image":["https://cdn.steemitimages.com/DQmPm3T8AegxZTkz5vF26BrhxXSkNxZxXu9WPFJaQkKJxez/imagen.png"],"app":"steemit/0.1"}
`created`	2019-04-27 20:54:48
`last_update`	2019-04-27 20:54:48
`depth`	1
`children`	1
`last_payout`	2019-05-04 20:54:48
`cashout_time`	1969-12-31 23:59:59
`total_payout_value`	0.000 HBD
`curator_payout_value`	0.000 HBD
`pending_payout_value`	0.000 HBD
`promoted`	0.000 HBD
`body_length`	93
`author_reputation`	3,266,503,388,440
`root_title`	"Matrices 2. Operaciones"
`beneficiaries`	`[]`
`max_accepted_payout`	1,000,000.000 HBD
`percent_hbd`	10,000
`post_id`	83,858,239
`net_rshares`	0

@josmar2511 · Apr 27 '19

Thank you @theclub!!

properties (22)