Matriz
Páginas: 6 (1394 palabras)
Publicado: 1 de marzo de 2012
1. 2A + 3B
2A = 2x
210 213 432 3 -1 0 2 1 4 2 2 2
=
420 426 864 9 -3 0 6 3 12 6 6 6
3B = 3x Luego
=
2A+3B=
4 2 0 4 2 6 8 6 4
+
9 -3 0 6 3 12 6 6 6
=
13 -2 0 10 0 -1 14 12 10
2. (A – B)(5B +A ) 210 213 432 3 -1 0 2 1 4 2 2 2 -1 2 0 0 0 -1 2 1 0
A–B=
-
=
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
5B = 5x
3-1 0 2 1 4 2 2 2
15 -5 0 = 10 5 20 10 10 10 210 213 432 17 -4 0 12 6 23 14 13 12
5B + A=
15 -5 0 10 5 20 10 10 10
+
=
→ (A – B)(5B +A ) =
1 2 0 0 0 -1 2 1 0
.
17 -4 0 12 6 23 14 13 12
→ (A – B)(5B +A ) =
-1+24+0 0+ 0-10 34+12+0 7 16 46 -14 -13 -12 46 -2 23
4+12+0 0 + 0 -13 -8+6+0
0+46+0 0+0-12 0+23+0
→ (A – B)(5B +A ) =
3. A.C+B.C 210 213 432 3 -1 0 21 4 2 2 2 -2 3 2 -4 6 -7 -2 3 2 -4 5 -7 -2 2 13 -19 3 -14 -6-2+0 -4+2+20 -4+4+10 9+4+0 6-9-28 6-8-14
A.C =
.
=
B.C=
.
=
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
→
-8 13 18 -26 10 -16
→ A.C+B.C =
-2 2 13 -19 3 -14
+
-8 13 18 -26 10 -16
=
-10 15 31 -45 18 -30
1. X-B2=A.B X=A.B+B2 A.B = 210 213 432 . 3 -1 0 2 1 4 2 2 2 =8 -1 4 14 5 10 22 3 16 7 -4 -4 16 7 12 14 4 12
B2 =BxB =
3 -1 0 2 1 4 2 2 2
.
3 -1 0 2 1 4 2 2 2
=
X=A.B+B =
2
8 -1 4 14 5 10 22 3 16
+
7 -4 -4 16 7 12 14 4 12
=
15 -5 0 30 12 22 36 7 28
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
2. f(A)=2A2 – 4A -5 210 213 432 210 213 432 4+2+0 4+2+12 8+6+8 2+1+0 2+1+9 4+3+6 0+3+0 0+3+6 0+9+4
A=AxA=
2
.
=
=
6 3 3 18 12 9 20 12 13 6 3 3 18 12 9 20 12 13 12 6 6 36 24 18 40 26 26
→2A = 2x
2
=
→4A= 4x
210 213 432 100 010 001
=
8 4 0 8 4 12 16 12 8 500 050 005
→-5= 5x
=
f(A)=2A2 – 4A -5
12 6 6 36 24 18 40 26 26 8 4 0 8 4 12 16 12 8 500 050 005 9 2 6 28 25 6 24 14 23
=
-
+
=
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca,Carlos
3. (A+B)t = At+ Bt 210 213 432 3 -1 0 2 1 4 2 2 2 500 427 654
A+B =
+
=
→(A+B) =
t
546 025 074 210 213 432
A=
→ A =
t
224 113 032
B=
3 -1 0 2 1 4 2 2 2
→ B =
t
3 2 2 -1 1 2 0 4 2 546 025 074
At+ Bt =
224 113 032
+
3 2 2 -1 1 2 0 4 2
=
→(A+B)t = At+ Bt 546 025 074 546 025 074
=
Acuña Ventosilla, Brayan AcedoCeña, Marvil Honores Vaca, Carlos
1. |A|+|B| 25 38 -3 -3 -5 4
A=
→
|A|= (
25 38 -3 -3 -5 4
=16 – 15 = 1
B=
→
|B|=
= -12 -15 = -27
→|A|+|B|= 1 +(-27)= -26/ 2. |C| -2 3 9 5 -4 4 3 3 -3 -2 3 9 5 -4 4 3 3 -3
C=
→ |C| =
= (-20+36+135)-(-108+ (-45)+ (-24))=120-(-177)=297/
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
3. |D|
D=
2 6 -51
-3 -3 6 -4
0 2 0 3
-4 1 3 2 -3 2 1 6 0 3 -4 3 2 -3 0 -4 6 0 3 -4 3 2
|D|
=(-1)1+1. (1)
+(-1)2+1. (-6)
+(-1) . (-5)
3+1
-3 0 -4 -3 2 1 -4 3 2
+(-1) . (-5)
3+1
-3 0 -4 -3 2 1 6 0 3
|D|=2{((-3)(0)(2)+(2)(3)(-4)+(6)(3)(1))-((1)(0)(4)+(2)(6)(2)+(3)(3)(-3))} =6{((-3)(0)(2)+(0)(3)(-4)+(6)(3)(4))-((-4)(0)(-4)+(0)(6)(2)+(3)(3)(-3))}=5{((-3)(2)(2)+(0)(1)(-4)+(-3)(3)(-4))-((-4)(2)(-4)+(0)(-3)(2)+(1)(3)(-3))} =1{((3)(2)(3)+(0)(1)(6)+(-3)(0)(-4))-((-4)(2)(6)+(0)(-3)(3)+(1)(0)(3))} |D|=2{(0-24+18)-(0+24-27)}-6{(0+0-72)-(0+0-27)}-5{(-12+0+36)(32+0-9)}-1{(18+0+0)-(-48+0+0)} |D|=2(-3)-6(45)-5(1)-66)= -6 + 270 - 5 - 66 = 193/
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
1. Adj |A| 1 1 3 2 -1 4 0 -1 1
A=
-1 4 -1 1 Adj(A)=
-
1 3-1 1 13 01
13 -1 4
- 01
2 -1 0 -1
2 4
-
13 24 1 1 2 -1
-
1 1 0 -1
(-1+4) -(1+3) Adj(A)= -(2-0) (-2-0) (1-0) -(-1-0)
(4+3) -(4-6) (-1-2) =
3 -4 -2 -2 1 1
7 2 -3
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
2. Adj |B| 5002 1102 0021 1001 102 021 001 Adj(B)= 102 021 101 112 001 101 110 002 100 002 021 001 502 021 101 502 001 101 500 002...
2A = 2x
210 213 432 3 -1 0 2 1 4 2 2 2
=
420 426 864 9 -3 0 6 3 12 6 6 6
3B = 3x Luego
=
2A+3B=
4 2 0 4 2 6 8 6 4
+
9 -3 0 6 3 12 6 6 6
=
13 -2 0 10 0 -1 14 12 10
2. (A – B)(5B +A ) 210 213 432 3 -1 0 2 1 4 2 2 2 -1 2 0 0 0 -1 2 1 0
A–B=
-
=
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
5B = 5x
3-1 0 2 1 4 2 2 2
15 -5 0 = 10 5 20 10 10 10 210 213 432 17 -4 0 12 6 23 14 13 12
5B + A=
15 -5 0 10 5 20 10 10 10
+
=
→ (A – B)(5B +A ) =
1 2 0 0 0 -1 2 1 0
.
17 -4 0 12 6 23 14 13 12
→ (A – B)(5B +A ) =
-1+24+0 0+ 0-10 34+12+0 7 16 46 -14 -13 -12 46 -2 23
4+12+0 0 + 0 -13 -8+6+0
0+46+0 0+0-12 0+23+0
→ (A – B)(5B +A ) =
3. A.C+B.C 210 213 432 3 -1 0 21 4 2 2 2 -2 3 2 -4 6 -7 -2 3 2 -4 5 -7 -2 2 13 -19 3 -14 -6-2+0 -4+2+20 -4+4+10 9+4+0 6-9-28 6-8-14
A.C =
.
=
B.C=
.
=
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
→
-8 13 18 -26 10 -16
→ A.C+B.C =
-2 2 13 -19 3 -14
+
-8 13 18 -26 10 -16
=
-10 15 31 -45 18 -30
1. X-B2=A.B X=A.B+B2 A.B = 210 213 432 . 3 -1 0 2 1 4 2 2 2 =8 -1 4 14 5 10 22 3 16 7 -4 -4 16 7 12 14 4 12
B2 =BxB =
3 -1 0 2 1 4 2 2 2
.
3 -1 0 2 1 4 2 2 2
=
X=A.B+B =
2
8 -1 4 14 5 10 22 3 16
+
7 -4 -4 16 7 12 14 4 12
=
15 -5 0 30 12 22 36 7 28
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
2. f(A)=2A2 – 4A -5 210 213 432 210 213 432 4+2+0 4+2+12 8+6+8 2+1+0 2+1+9 4+3+6 0+3+0 0+3+6 0+9+4
A=AxA=
2
.
=
=
6 3 3 18 12 9 20 12 13 6 3 3 18 12 9 20 12 13 12 6 6 36 24 18 40 26 26
→2A = 2x
2
=
→4A= 4x
210 213 432 100 010 001
=
8 4 0 8 4 12 16 12 8 500 050 005
→-5= 5x
=
f(A)=2A2 – 4A -5
12 6 6 36 24 18 40 26 26 8 4 0 8 4 12 16 12 8 500 050 005 9 2 6 28 25 6 24 14 23
=
-
+
=
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca,Carlos
3. (A+B)t = At+ Bt 210 213 432 3 -1 0 2 1 4 2 2 2 500 427 654
A+B =
+
=
→(A+B) =
t
546 025 074 210 213 432
A=
→ A =
t
224 113 032
B=
3 -1 0 2 1 4 2 2 2
→ B =
t
3 2 2 -1 1 2 0 4 2 546 025 074
At+ Bt =
224 113 032
+
3 2 2 -1 1 2 0 4 2
=
→(A+B)t = At+ Bt 546 025 074 546 025 074
=
Acuña Ventosilla, Brayan AcedoCeña, Marvil Honores Vaca, Carlos
1. |A|+|B| 25 38 -3 -3 -5 4
A=
→
|A|= (
25 38 -3 -3 -5 4
=16 – 15 = 1
B=
→
|B|=
= -12 -15 = -27
→|A|+|B|= 1 +(-27)= -26/ 2. |C| -2 3 9 5 -4 4 3 3 -3 -2 3 9 5 -4 4 3 3 -3
C=
→ |C| =
= (-20+36+135)-(-108+ (-45)+ (-24))=120-(-177)=297/
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
3. |D|
D=
2 6 -51
-3 -3 6 -4
0 2 0 3
-4 1 3 2 -3 2 1 6 0 3 -4 3 2 -3 0 -4 6 0 3 -4 3 2
|D|
=(-1)1+1. (1)
+(-1)2+1. (-6)
+(-1) . (-5)
3+1
-3 0 -4 -3 2 1 -4 3 2
+(-1) . (-5)
3+1
-3 0 -4 -3 2 1 6 0 3
|D|=2{((-3)(0)(2)+(2)(3)(-4)+(6)(3)(1))-((1)(0)(4)+(2)(6)(2)+(3)(3)(-3))} =6{((-3)(0)(2)+(0)(3)(-4)+(6)(3)(4))-((-4)(0)(-4)+(0)(6)(2)+(3)(3)(-3))}=5{((-3)(2)(2)+(0)(1)(-4)+(-3)(3)(-4))-((-4)(2)(-4)+(0)(-3)(2)+(1)(3)(-3))} =1{((3)(2)(3)+(0)(1)(6)+(-3)(0)(-4))-((-4)(2)(6)+(0)(-3)(3)+(1)(0)(3))} |D|=2{(0-24+18)-(0+24-27)}-6{(0+0-72)-(0+0-27)}-5{(-12+0+36)(32+0-9)}-1{(18+0+0)-(-48+0+0)} |D|=2(-3)-6(45)-5(1)-66)= -6 + 270 - 5 - 66 = 193/
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
1. Adj |A| 1 1 3 2 -1 4 0 -1 1
A=
-1 4 -1 1 Adj(A)=
-
1 3-1 1 13 01
13 -1 4
- 01
2 -1 0 -1
2 4
-
13 24 1 1 2 -1
-
1 1 0 -1
(-1+4) -(1+3) Adj(A)= -(2-0) (-2-0) (1-0) -(-1-0)
(4+3) -(4-6) (-1-2) =
3 -4 -2 -2 1 1
7 2 -3
Acuña Ventosilla, Brayan Acedo Ceña, Marvil Honores Vaca, Carlos
2. Adj |B| 5002 1102 0021 1001 102 021 001 Adj(B)= 102 021 101 112 001 101 110 002 100 002 021 001 502 021 101 502 001 101 500 002...
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