Jacobcastillo20920329
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Transcript of Jacobcastillo20920329
ALGEBRA LINEAL
JACOB CASTILLO. C.I: 20920329
Usando algoritmo de Gauss-Jordan determina si la siguiente matriz es invertible. En caso de serlo calcule su inversa.
1. A= [−14
1 6
−5 −83
7
1 3 29]
Planteamos lo siguiente:
(−14
1 6
−5 −83
7
1 3 29|1 0 00 1 00 0 1)
f 3❑↔f 1: (
1 3 29
−5 −83
7
−14
1 6|0 0 10 1 01 0 0)
2da f : 5 f 1−f 2:
(1 3 2
9
0 533
−539
−14
1 6 |0 0 10 −1 51 0 0)
f 3: 14 . f 1 + f 3
(1 3 2
9
0 533
−539
0 74
10918
|0 0 10 −1 5
1 0 14 )
f 2: 3
53f 2:
(1 3 2
9
0 1 −13
0 74
10918
|0 0 1
0 −353
1553
1 0 14 )
f 3: 74f 2−f 3 :
(1 3 2
9
0 1 −13
0 0 −23936
| 0 0 1
0 −353
1553
−1 −21212
1353 )
f 1: −3 f 2+ f 1:
(1 0 11
9
0 1 −13
0 0 −23936
| 0 953
853
0 −353
1553
−1 −21212
1353
)f 3:
−36239
f 3 :
(1 0 119
0 1 −13
0 0 1 | 0 953
853
0 −353
1553
36239
18912667
−46812667
)f 2:
−13f 3+ f 2 :
(1 0 119
0 1 00 0 1 | 0 9
538
5312
239−34662671351
181737671351
36239
18912667
−46812667
)f 1:
−119f 3+f 1:
(1 0 00 1 00 0 1|
−44239
3052802014053
118486860421559
12239
−34662671351
181737671351
36239
18912667
−46812667
)La matriz inversa es:
A−1 =(−44239
3052802014053
118486860421559
12239
−34662671351
181737671351
36239
18912667
−46812667
)
II. Determinar la traza de la siguiente matriz:
3)
Tr(C) = -6 +0+ (-4) = -10.
III. Determine los valores de λ para los cuales existe la inversa de la matriz
5.)
|E| = |−3 −1 20 λ 3
−43
2 1|= |λ 32 1|= λ.1-2.3 = λ-6 ⇒ λ=6
Si λ≠ 6 E es invertible.
V. Encontrar la matriz A sabiendo que (4. A )−1 = [ 2 3−4 −4]
Aplicando la propiedad la inversa del producto de dos matrices, tenemos.
A−1. 4−1 = [ 2 3−4 −4]
Luego, A−1. 14 =[ 2 3
−4 −4]A−1= 4[ 2 3
−4 −4]A−1 =[ 8 12
−16 −16 ]Entonces A = [−16 −12
16 8 ]