Exam (elaborations)
Ejercicios - Operaciones entre matrices
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Inversa de una matriz, Multiplicación entre matrices, Propiedades de las matrices y sistemas matriciales
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SEMANA 3Ejercicios adicionales (MA1116)
1. Halle los valores de a, b, c, d, e y f , de forma tal que se satisfaga que
a 0 0 1 0 5 1 0 5
b c 0
−1 −1 −8 = 0 −1 .
−3
d e f 1 3 12 0 0 −2
2. Resolver el sistema de ecuaciones lineales
X2 Z k
xj xj = k, con k = 1, 2, 3.
j=1 0
ax − 2y + z = 1
3. Sea el sistema de ecuaciones lineales x + ay + 2z = a . Encuentre los valores de “a” para
x + z=1
que el sistema dado tenga: solución única, infinitas soluciones y no tenga solución.
4. Suponga que A, B y X son matrices cuadradas de orden n, con A y B conocidas e invertibles.
(a) Resuelva utilizando las propiedades de las operaciones de matrices la siguiente ecuación matri-
cial:
X B A + A2 − X B − B 2 A − B 2 A = A.
(b) Calcule la solución de la ecuación matricial dada en el caso en que
1 −1 0 1 0 0
A= 0 1 −1 , B= −1 1 .
0
0 0 1 0 −1 1
!
−1 1
5. Considere la matriz A=
2 3
(a) Plantee un sistema de ecuaciones lineales que permita encontrar todas las matrices
!
x y
B= ,
z w
tales que el producto AB sea una matriz antisimétrica.
(b) Resuelva el sistema planteado en el apartado 5a) y escriba la expresón para la matriz B.
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