linear_equations_and_matrices(question).pdf
TRANSCRIPT
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E-learning 03 -03-55
1
1. x y
1 2 3 2 3
2 1 2 3
3 2 1 2 3
x
A x B y
y
A B x y (PAT 1 2551 ) 1. 1 2. 2 3. 3 4. 4
2. 1 2 1
2 2
2 1
A x
y
x y
11( ) 13C A 21( ) 9C A det( )A ( PAT 1 2552 ) 1. 33 2. 30 3. 30 4. 33 3. A 4 4 ( )ijM A ija 23( ) 5M A 32 (2 )tM A (Ent. . 2538) 1. 10 2. 20 3. 40 4. 80
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E-learning 03 -03-55
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4. , A B 3 3 I 3 3
AB BA I 1 1 1
2 1 3
1 0 1
A
B
1. 13A 2. 3A
3. 13
tA 4. 3 tA 5. , , A B C I 3 3 1A B A C , 2AC C 2 2det( ) 2A C det(3 ( ))adj B 1. 27 2. 36 3. 54 4. 108 6. 1 2 1 1 ,
3 4 2 1A B
12 tA B ( Ent. . 2541 ) 1. 2 10
2 7
2. 2 102 7
3. 5 26 6
4. 5 2 6 6
7. A I 3 3
1 2 1
3 0 1
2 1 0
B
0 2 3
3 1 2
0 2 1
C
1 02
AB AC I 1A ( Ent. . 2537 )
1. 1 0 2
0 1 1
2 1 1
2. 2 0 4
0 2 2
4 2 2
3. 1 0 2
0 1 1
2 1 1
4. 2 0 4
0 2 2
4 2 2
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E-learning 03 -03-55
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8. 1 6
2 5 7
4 2 9
x
A
y
32a 23 23a
44 x y ( Ent. 1/1 2544 ) 9. A 3 3 13 211 3 1 1 , 1 2 2 4M M
32 2 1 1 0M det( )A ( Ent. 1 2542 ) 10. A B 2 2 1 1det( )
2A
1 2
Bx y
x y 3 2AB A I x y ( Ent. . 2536 ) 1. 2 2. -2 3. 4 4. -4
11. 2 11 3
A
3 3
7
x xM
x
x
1det det (2 )tM A A A ( Ent. . 2541 ) 1. 11 , 5
7
2. 11 , 57
3. 11 , 57
4. 11 , 57
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E-learning 03 -03-55
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12. 3 41 2
A
30 1812 8
C
B AB C ( Ent. . 2541 ) 1. 1det( ) 12B 2. 1 1det( ) 24B A 3. det(2 ) 24tB 4. 2det( ) 48A B
13. 1 1
3 1 1
0 1
x
A
x
12 ( ) 4C A det(2 )A ( A-NET 2550 )
14. 1
2
3
1 1 2
1 1 ,
1 1
x
A a X x
a x
1
0
1
B
a
AX B ( )x ( Ent. . 2541 ) 1. 1R 2. 1, 2R 3. 3R 4. 1,3R 15. , , x y z 2 2 1x y z 3 7x y z 5x y z 1 2 3
x y z ( PAT 1 2552 )
1. 0 2. 2 3. 5 4. 8
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E-learning 03 -03-55
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16. 1 11 1
A
x yB
y z
1 2 0 0 4
A BA
xyz ( 2553 ) 1. 3 2. 1 3. 0 4. 1
17. 1 2 3 1
1 2 3 2
31 2 3
41 2 3
0
0 ,
1
2
a a a x
b b b xA X
xc c c
xd d d
0
0
2
1
B
41det 8 , ( ) 2A C A AX B 1x ( . . 2554)