EXAMENES_ALGEBRA_LINEAL_I.docx - ESCUELA POLITÉCNICA DEL EJÉRCITO VICERRECTORADO ACADÉMICO DEPARTAMENTO DE CIENCIAS EXACTAS ÁLGEBRA LINEAL 1 HALLAR

# EXAMENES_ALGEBRA_LINEAL_I.docx - ESCUELA POLITÉCNICA DEL...

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ESCUELA POLITÉCNICA DEL EJÉRCITO VICERRECTORADO ACADÉMICO DEPARTAMENTO DE CIENCIAS EXACTAS ÁLGEBRA LINEAL 1.- HALLAR LA MATRIZ A, DADA: adj ( A ) = ( 1 2 3 4 0 5 2 3 0 0 5 1 0 0 0 5 ) 2.- SEA A n TAL QUE A 2 = A . SEA B = 2 A I a) HALLAR B 2 EN FUNCIÓN DE A e I, LUEGO HALLE B 1 b) HALLE B n EN FUNCIÓN DE a e I. 3.- DEMOSTRAR UTILIZANDO ÚNICAMENTE PROPIEDADES QUE: | bc a 2 a 2 b 2 ca b 2 c 2 c 2 ab | = | cb ab ac ab ca bc ca bc ab | 4.- HALLAR LOS VALORES DE a Y b PARA QUE EL SISTEMA TENGA: { x + y + z = 1 2 x + ( 3 + a ) y + ( 2 + a ) z = 1 3 x + 3 y + ( 4 + 2 a ) z = ( 3 + b ) a) SOLUCIÓN ÚNICA b) INFINITAS SOLUCIONES c) NO EXISTE SOLUCIÓN PRESENTE EL CONJUNTO SOLUCIÓN EN CADA CASO. ÁREA DE ANÁLISIS TERCERA UNIDAD

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ESCUELA POLITÉCNICA DEL EJÉRCITO VICERRECTORADO ACADÉMICO BANDA: MARTES 07:15-09:13 DEPARTAMENTO DE CIENCIAS EXACTAS ÁLGEBRA LINEAL 1.- ESTUDIAR EL RANGO DE LA SIGUIENTE MATRIZ, SEGÚN LOS PARÁMETRO DADOS: A = ( a 1 2 0 a 0 0 0 b ) 2.- DEMOSTRAR APLICANDO ÚNICAMENTE LAS PROPIEDADES QUE: | a a a a a b b b a b c c a b c d | = a ( a b ) ( c b ) ( c d ) 3.- HALLAR LOS VALORES DE a Y b PARA QUE EL SISTEMA TENGA:
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