EVALUACIÓN PARCIAL ALGEBRA MATRIACAL
Rodrigo Americo Lastra LoarteTrabajo19 de Noviembre de 2020
8.975 Palabras (36 Páginas)138 Visitas
[pic 1]
EVALUACIÓN PARCIAL
ASIGNATURA[pic 2]
FACULTAD : INGENIERÍA ALUMNO:
INSTRUCCIONES:[pic 3]
- OPERACIONES CON MATRICES:
Dadas las matrices:
[pic 4]
Calcula:
- [pic 5]. (2 puntos)
- Traza de la matriz X. (1 punto)
Solución:
[pic 6][pic 7]
a11 a12 a13 -2 0 -2 [pic 8][pic 9]
A = a21 a22 a23 A = 0 2 0[pic 10]
a31 a32 a33 -2 0 -2
aIJ = (-1)i + (-1)j
a11 = (-1)1 + (-1)1 = -2 a12 = (-1)1 + (-1)2 = 0 a13 = (-1)1 + (-1)3 = -2
a21 = (-1)2 + (-1)1 = 0 a22 = (-1)2 + (-1)2 = 2 a23 = (-1)2 + (-1)3 = 0
a31 = (-1)3 + (-1)1 = -2 a32 = (-1)3 + (-1)2 = 0 a33 = (-1)3 + (-1)3 = -2
[pic 11][pic 12]
b11 b12 b13 2 3 4 [pic 13][pic 14]
B = b21 b22 b23 B = 3 4 5[pic 15]
b31 b32 b33 4 5 6
bIJ = i + j
b11 = 1 + 1 = 2 b12 = 1 + 2 = 3 b13 = 1 + 3 = 4
b21 = 2 + 1 = 3 b22 = 2 + 2 = 4 b23 = 2 + 3 = 5
b31 = 3 + 1 = 4 b32 = 3 + 2 = 5 b33 = 3 + 3 = 6
- X = 2A + 3B - 5I
[pic 16][pic 17][pic 18][pic 19][pic 20][pic 21]
X = 2 -2 0 -2 + 3 2 3 4 - 5 1 0 0
0 2 0 3 4 5 0 1 0
-2 0 -2 4 5 6 0 0 1
[pic 22][pic 23][pic 24][pic 25][pic 26][pic 27]
X = -4 0 -4 + 6 9 12 - 5 0 0
0 4 0 9 12 15 0 5 0
-4 0 -4 12 15 18 0 0 5
[pic 28][pic 29][pic 30][pic 31]
X = 2 9 8 - 5 0 0
9 16 15 0 5 0
8 15 14 0 0 5
[pic 32][pic 33][pic 34]
X = -3 9 8
9 11 15
8 15 9
- Traza de la matriz X:
[pic 35][pic 36][pic 37]
-3 9 8 [pic 38][pic 39]
X = 9 11 15 X = -3 + 11 + 9 = 17
8 15 9
- Calcula la determinante de la matriz A. (3 puntos)
[pic 40]
Solución:
[pic 41][pic 42]
1 1 0 0 0
A = 1 1 0 0 0
1 1 0 0 0
1 1 0 0 0
1 1 0 0 0
0 + 2 x (+) 1 1 0 0 + 1 x - 1 1 0 0 + 0 + 0[pic 43][pic 44][pic 45][pic 46]
0 2 0 7 2 5 -2 5
3 0 4 9 3 0 4 9
0 0 -4 11 0 0 -4 11
...