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Summary

Sumario Apuntes Matrices (BI)

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Apuntes del tema de Matrices del temario de Matemáticas II. Con ejemplos y explicaciones claras para el examen de PAU.

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ordenadodenúmeros
Matriz conjunto
asonasecundaria

a
am ama
manenficasyncolumnas diagonalprincipal


tipos
cuadrada mismonúmerofilasycolumnas

triangularsuperior términosdebajodiagonalprincipal O
2 a
triangularinferior términosencima
diagonalprincipal o
nuca todoslostérminossono

identidad diagonalprincipalconeye resto a

diagonal todoomenosdiagonalprincipal

escalar diagonalcontodoslostérminosde ladiagonalprincipaliguales_a

gira sacounagira a c 3 1 21

columna solo una columna a

simétrica haysimetríarespectodeladiagonalprincipal
a
antisimétrica simétricaperocambiadadesigno

traspuesta intercambiadasfilasycolumnas a at


orden navarvaloresapartirdeunaexpresión

matrizdeorden n min orden
3 2 2.1 5.2 12

operaciones

sumayresta mismonúmeroman




multiplicaciónporescalar
a nA

,multiplicacióndematrices

elnúmerodecolumnasdeatienequecoincidirconelnúmerodefilasdeB amxn.brxp

obtieneso connogirasa ynocolumnasB Amin Bnxp amxp


aaxa.Ba.ae


ca a carta 4 0 21 110 al noesconmutativa Axa Baro
Baxianzxa

potenciaan A a A




divisióndematrices a a 1 1 buscasquetedé lamatriz I asiquebuscasla matrizinversaa

1ADIC unamatrizsolotieneinversasiescuadrada
I o
notodaslasmatricescuadradastieneninversa

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iii
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a navaran

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in eams

i a Dividirparanegarazencaizquierda I
1 0 117217
esa es a o a 317117

, EJERCICIOS




a



a 131 41.5 3.13141 13010401 e a 3 121 c aorta421 11121 ya
cuandotienesunnúmero


I a al se ex nee n x as se c este sina.ca ii E a




a Btc B a c A A B c 9
a a a B atea necesariamenteasiquenosenaceasi
q EE EEEIEIEI I IesBr


NOSECUMPLE



Fa Fa are Fa 3Fa ar Fatara 3Er

Fi 3Er Fi nantara Fi AR 3Er


FrayFaiz FeistyFalta 3,4 Fila yFama




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Study
Bachillerato
School year
6
Uploaded on
June 15, 2025
Number of pages
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Summary
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