More Related Content More from Nittaya Noinan (20) แบบฝึกหัดเมทริกซ์2. 40
1.
-
1.
x + 3y
x – 2y
=
=
8
3
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3. 2.
x- y
=
2x + 3y =
-4
22
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3.
x+ y+z
=
6
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x–y+z
= 2
……………………………. =
x+y-z
0
5. 4.
x + 2y
-z =
3
3x + y
=
6
2x + y
=
1
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6. 5.
2x - 3y + z
=
8
- x + 4y + 2z
=
-4
3x - y + 2z
=
9
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7. 6.
x - y + 2z
=
-3
y – 3z
=
5
x + 4y – 8z
=
17
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9. 7.
x + y
=
2
x + 3y + z
=
5
3x + y - z
=
3
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10. 8.
2x + 2y + 3z + 2t =
-3
x + y + 2z + 2t
=
6
2y + 5z + 2t
=
5
x + y + 3z + 4t
=
1
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14. 3
1.
1.
4 1
7 9
……………………..
3 1 1 3
2.
0 2 2
1
0 0 3 0
0 0 0 6
……………………..
3.
2 3 4
……………………..
4.
2 0
0 2
……………………..
5.
0 0 0
0 0 0
……………………..
15. 2.
1)
2 3 2
2)
0 1 4
2 5
3)
1 0
0 1
9)
6 2
0 3
0 0 1
4)
0 0
0 0
5)
0 1
1 0
6)
1 0 0
0 1 0
0 0 1
7)
0 0 0
8)
0 0 0
0 0 5
12)
0
1
8
. 10)
5
0
1
2
14)
0 0 0
15)
9
0
0
8
5
0
3
0 2 0
0 0 2
3
13)
2 0 0
1
5
11)
0
.
17. 1.
A
1
2
2x
6
1
, B
A = B
y
8 3 2
x
y
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3x y
2
1
2
2.
……………
A
x = A = B
2y
, B
5
y =
10
x
5
y
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3.
……………
x =
A = B
A
o
4
3
8
y =
, B
x
x
x
3
y
8
y
x = ……………
y = ……………
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18. 3
4.
A
1
4
2
0
1
x
4
0
8
2 5
8 , B
x 5
A = B
3
4
4
x
y
y
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1 9
2
3 3x 2 x y
5.
……………
3
4
5
2 5
x =
A
4
y =
A = B
, B
3
4 5
2 5 4
x
y
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19. 6.
A
x
y
x
y
A = B
1
, B
7
x
y
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A
, B
7.
2x
……………………
x =
A = B
x
y
5
y
y =
1
x
y
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20. 8.
A
x
y
x 2y
, B
A = B
8
1
x
y
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x =
9.
A
A = B
y2 x= 2 y
4x
y
, B
x
2
4
y
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21. 10.
A
A = B
3x 2 y
x 4y
, B
x
1
7
y
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22. 8
1.
A =
1
0
2 4
At
5 3
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2.
B =
1 7 0
Bt
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23. 3.
C =
2 3 0
Ct
1 5 1
7 4 5
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4.
D =
1 2 3 4
Dt
5 6 7 8
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5.
E =
2
3
Et
4
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24. 6.
G =
0 3 6
1 4 7
Gt
2 5 8
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7.
A =
2 1 0
0 5 3
2 4 3
B =
1 4 2
3 2 0
(A +
1 5 9
B)t
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25. 8.
A =
2 1 0
0 5 3
2 4 3
B =
1 4 2
3 2 0
At +
1 5 9
Bt
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26. 9.
A =
1 2
3 0
B =
5
4
1
2
(AB)t
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…………………………. 2
1
5
1
10.
A =
B =
BtAt
3 0
4
2
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30. 2.5 -4A - 2B =…………………………………….
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31. 6
X
1.
X
A =
1 3
2 4
,B =
0 3
1 5
2X = 2A + 2B
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0 0
.................................................... , B = 2 4
2.
A =
0 0
5
3
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X
3X – 3B = 2A
32. 3.
A =
3 4
2 6
X
,B =
1
4
2 6
X – A = 3B
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33. 4.
A =
4 3
1
2
,B =
0 1
3 0
X
-2A - X = -3B
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6 4
5.
A =
X
.........................................................
2 0
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A + X = 2A – X
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34. A =
2 6
0
4 4
2
6.
4
2 0
2
3
5
0
2
1
,B =
1
1
1
X
A+ X = B
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35. A =
4
1
2
1
1
1
7.
1
2
1
,B =
1
1
1
3
2
1
2
5
1
X
2A - X = 3B
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3 8
1 0
8.
A =
,B =
0 1
0 1
....................................................
X
..............................................................................................
- (A + 3B) = X
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36. A =
6
2
0
10
0
2
9.
0
4
2
,B =
2
1
0
3
3
5
4
9
1
X
2(A + 2X) = 4B
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0 0
1
5
10.
A =
,B =
0 0
0
2
....................................................
X
..............................................................................................
-2
.................................................... ( 2A – X) = 2B + X
38. 1.
A =
1 3 5
B =
2
4
AB
6
AB =
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………..
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………..
5
1
2
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2.
A =
B =
AB
………..
0
2
3
AB =
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39. 3.
A =
1 2
3 4
B =
0
2
1
5
AB
AB =
……………………………………………………………………
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………..
3 5
0
1 4
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4.
A =
B =
AB
7 0
2
3 5
……….
AB =
……………………………………………………………………
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40. 5.
A =
1
2
2 0
3 4
B =
4
5
1
2
0
1
BA
BA =
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41. 1
6.
4
A =
B =
5
2 0
AB
1
2
AB =
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……….
2
1 3
7
4
7.
A =
B = 5 0
AB
3
0 5
0
3
……………………………………………………………………
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AB =
……………………………………………………………………
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43. 9.
A =
1 0
0 1
B =
5
2
4
3
AB
AB =
……………………………………………………………………
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………..
1 0
5
4
10.
A =
B =
BA
……………………………………………………………………
0 1
2
3
………..
BA =
……………………………………………………………………
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44. 9
1.
A =
1 0
2 3
,B =
0 2
2 1
,C =
1 1
4 5
(AB)C = A(BC)
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45. 2.
– B2
A =
1 1
2 3
,B =
0 2
1 1
A2
(A - B)(A + B)
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48. 4.
+ B)2
A =
2 1
0 3
,B =
1
1
2
4
(A
A2+2AB + B2
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49. 5.
A =
0 3
1 2
,B =
0 1
5 2
(AB)t = BtAt
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50. 6.
A =
1 0
2 5
, B =
1 2
3 4
(A + B)C = AC + BC
, C =
0 1
4 0
52. 7.
A =
2 1
3 0
(At)t = A
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3 8
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8.
A =
(3A)t = 3At
0 1
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53. 9.
A =
6 1
7 0
,I =
1 0
0 1
IA = A
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0 0
1
10.
A =
,B =
0 0
0
2
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X
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-2 ( 2A – X) = 2B + X
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1 2
6
2
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10.
A =
, B =
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55. 1.
A =
1 2
0 3
A
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1 2
2.
A =
A
1 0
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57. 5.
A =
1 2
3 4
A
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4 3
6.
A =
A
1 2
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58. 2
B
A
2
1.
A =
3 2
1 4
, B =
4
2
1
3
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60. A =
1
1 0
2
3 1
2.
2 1
1
, B =
2 0
2
7 1
5
1 1
1
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61. 3
3A - 3B =
A-1
1
1
B-1
A + B =
3 1
1 2
1
0
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62. 4
2A-1 - B-1 =
A
B
A-1 + B-1 =
2
2
1 3
1 1
4 3
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67. 3
1 2
1
2 0
2.
0 3
5
=……………………………………………………………
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=……………………………………………………………
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=……………………………………………………………
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3.
2 1 4
1 0 2
5 3 1
=………………………………………………………
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=………………………………………………………
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68. 1 0
5
2 0
8
4.
2
3 7
=……………………………………………………………
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=……………………………………………………………
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=……………………………………………………………
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=……………………………………………………………
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5 3
2
……………………………………………………………
4 0
1
5.
….. 2 4 2
=……………………………………………………………
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=……………………………………………………………
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=……………………………………………………………
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=……………………………………………………………
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69. 12
1.
A =
2 0 5
3 1 3
det (A) =
4 2 2
det(At)
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70. 2.
A =
2 0 0
8 1 0
det (A) =
4 9 2
a11a22a33
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71. 3.
A =
2 3
1 0
,B =
8 12
1 0
det(B) = 4 det(A)
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72. 4.
A =
5 4
2 2
,B =
10 8
4 4
det(B) = 22 det(A)
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1 0 0
73. 6.
A =
3 5
4 6
det(A-1) =
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74. 7.
A =
1 6
2 3
,B =
4
8
3
5
det(AB) = det(A)det(B)
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75. 8.
A =
0
2
1 7
det(A3) =
det(A)3
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76. 9.
A =
1 2 3
3 4 2
5 6 0
det(A) = det(B)
, B =
1
2
3
6 10 11
5
6
0
78. A =
2
3 5
7
1 0
10.
2 4
1
, B =
2 4 2
7 5 3
1 0 1
det(A) = - det(B)
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81. 5.
B =
1 0 2
5 3 4
M23(B)
1 2 5
6.
C =
2 0 1
1 2 4
3 6 0
M33(C)
82. 8.
A =
B =
4
3 1
5
0 1
7.
1 2
2
1 0 2
5 3 4
M13(A)
M31(B)
1 2 5
9.
C =
2 0 1
1 2 4
3 6 0
M13(C)
83. 1 2 3 4
10.
A =
0 1 5 7
1 2 6 0
2 4 3 8
M34(A)
86. 5.
A =
B =
4
3 1
5
0 1
4.
1 2
2
1 0 2
5 3 4
C13(A)
C33(B)
1 2 5
6.
C =
2 0 1
1 2 4
3 6 0
C21(C)
88. 9.
C =
2 0 1
1 2 4
C31(C)
3 6 0
1 2 3 4
10.
A =
0 1 5 7
1 2 6 0
2 4 3 8
C14(A)
93. A =
4
3 1
5
0 1
7.
0 2
2
det(A)
2 3 7
8.
B =
0
1 2 6
1
0 0 0
4
4 1 3
0
det(B)
95. 1 0 3 0
10.
A =
0 1 5 7
1 2 6 0
2 4 3 8
det(A)
99. A =
2 1
4
5 6
2
5.
3
3 1
adj (A)
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3
4
2
6
3
1
6.
B =
adj (B)
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4
7
8
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100. A =
1
3
1 12
4
1
7.
5
3
6
adj (A)
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101. 8.
B =
10
5
30
0 10
0 10
5
adj (B)
1
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7
3
3
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1
1
0
9.
A =
adj (A)
…………………….
1
0
1
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102. 4 8 8 4
10.
B =
1 2 0 2
0 1 2 3
adj (B)
2 4 1 4
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103. 17
1.
A =
1 0
5 3
A-1 (
(1
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104. 2.
A =
1 5
2 6
A-1 (
(1
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116. 18
1.
2x - 3y
= -1
10x + y = 11
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117. 2.
3x - 6y
= 2
5x + 4y = 1
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118. 3.
4x - 7y
= -2
- x + 2y = 1
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120. 4.
8x + 6y = -6
-2x + 4y = -26
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121. 5.
x + 3y
=
4
-2x - 4y
=
-6
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122. 6.
x + y
- z = -1
4x - 3y + 2z = 16
2x - 2y - 3z = 5
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125. 8.
4x + y
= 6
2x - y + 4z = 12
-3x + 2y + z = 4
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126. 9.
x + y + z
= 5
2x - y + 2z = 4
3x + 2y - z = -3
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129. 19
1.
2x - 3y
= -1
10x + y = 11
……………………………………………………………………
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130. 2.
3x - 6y
= 2
5x + 4y = 1
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131. 3.
4x - 7y
= -2
- x + 2y = 1
……………………………………………………………………
133. 4.
8x + 6y = -6
-2x + 4y = -26
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134. 5.
x + 3y
=
4
-2x - 4y
=
-6
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135. 6.
x + y
- z = -1
4x - 3y + 2z = 16
2x - 2y - 3z = 5
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137. 7.
6x + y
+ 20z
x - y
= 27
= 0
y + 3z = 4
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138. 8.
4x + y
= 6
2x - y + 4z = 12
-3x + 2y + z = 4
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139. 9.
x + y + z
= 5
2x - y + 2z = 4
3x + 2y - z = -3
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142. 20
1.
x + y
- z = -1
4x - 3y + 2z = 16
2x - 2y - 3z = 5
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143. 2.
2x + 4y - 2z = 0
3x + 5y = 1
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146. 4.
x + 2y
+ z= 8
3x + 7y + 6z
= 26
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147. 5.
4x + y
= 6
2x - y + 4z = 12
-3x + 2y + z = 4
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148. 6.
x + y + z
= 5
2x - y + 2z = 4
3x + 2y - z = -3
150. 7.
x + 2y
= 0
z
= -4
x + 3y
+
4x
w
= 4
+ 2w
= -2
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151. 8.
x - 3z
= -2
3x + y - 2z
=
2x + 2y + z
= 4
5
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152. 9.
x + 5y + 2z
= 6
2x + 10y + 2z
x + 5y + z
=
6
= 3
4x + 20y + 5z
= 15
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154. 10.
4w + x + 2y + 2z= 11
12w + 3x + 6y + 5z
= 30
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