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Jawapan matriks spM LATIH TUBI 2015
- 1. Soalan Penyelesaian dan Skema Markah Markah
1. a) (1)6 - k(2) = 0
– 2k = -6
K = 3
b) (i) Matrikssongsang=
12
26
)2(2)6(1
1
=
12
26
2
1
=
2
11
13
ii)
62
21
y
x
=
4
1
y
x
=
12
26
)2(2)6(1
1
4
1
=
)4(1)1(2
4)2()1(6
46
1
=
2
2
2
1
=
1
1
Maka, x = -1,y = 1
P1
P1
P1
K1
N1 N1
1
1
1
1
2
6
Markah
2. a) K(3) – (-4)(1) = 0 , (ad-bc= 0)
3k + 4 = 0
K = 3
4
b) Q-1 =
31
51
)1(5)1(3
1
=
31
51
2
1
=
2
3
2
1
2
5
2
1
c) Q
y
x
=
2
14
11
53
y
x
=
2
14
y
x
=
31
51
)1(5)1(3
1
2
14
P1
K1
N1
P1
1
1
1
1
- 2. =
2)3()14(1
2)5()14(1
53
1
=
8
4
2
1
=
4
2
Maka x = 2 , y = 4
3.
a)
n3
21 -1 =
13
2
)3)(2()(1
1 n
n
=
13
2
6
1 n
n
=
6
1
62
3
6
2
6
n
nn
n
.
Diberi
m3
25
=
6
1
62
3
6
2
6
n
nn
n
5 =
𝒏
−𝒏+𝟔
-5n + 30 = n
6n = 30
n = 5
Masukkan n = 5 dalam m =
−𝟏
−𝒏+𝟔
m =
−𝟏
−𝟓+𝟔
= -1
Maka n = 5, m = -1
4.
a)
13
24 -1 =
43
21
3)2()1(4
1
=
43
21
64
1
=
2
2
3
1
2
1
- 3.
nm
1
2
1
=
2
2
3
1
2
1
Maka m = 2
3
, n = 2)
b) 4x 2y = 10
3x y = 6
13
24
y
x
=
6
10
y
x
=
43
21
)3)(2()1(4
1
6
10
=
)6(4)10(3
)6(2)10(1
64
1
=
6
2
2
1
=
3
1
Maka x = , y= -3
5.
a)
65
43 -1 =
35
46
)5)(4()6(3
1
=
35
46
2
1
Diberi
35
6 p
m =
35
46
2
1
Maka m =
1
2
, p = 4
b) 3x 4y = 1
5x 6y = 2
65
43
y
x
=
2
1
y
x
=
35
46
)5)(4()6(3
1
2
1
- 4. =
)2(3)1(5
)2(4)1(6
2018
1
=
11
14
2
1
=
5.5
7
Maka x = 7 , y = 5.5
6.
a)
1
2
n
m -1 =
2
1
)()1(2
1
n
m
nm
=
2
1
2
1
n
m
mn
Diberi matriks songsang
2
31
8
1
n
= =
2
1
2
1
n
m
mn
m = 3
Masukkan m =3 dalam(8 = 2-mn)
8 = 2 – 3n
n = -2
Maka m = 3 , n = -2
b)
8
16
k
h
M
12
32
k
h
=
8
16
k
h
=
22
31
)2(3)1(2
1
8
16
=
)8(2)10(3
)8)(3()16(1
62
1
=
16
40
8
1
=
2
5
Maka h = 5 , k = 2
- 5. 7.
a) M-1 =
65
32
5)3()2(6
1
Diberi
65
3
15
1 a
ab
=
65
32
5)3()2(6
1
a = -2
masukkana = -2 dalamab = -12
-2b = -12
b = 6
Maka a= -2 , b = 6
b)
2
0
f
e
M
25
36
2
0
f
e
f
e
=
65
32
5)3()2(6
1
2
0
=
)2(6)0(5
)2(3)0(2
1512
1
=
12
6
3
1
=
4
2
Maka e = 2 , f = 4
8. a) 2p + 7 q = -2
3p + 8q = 3
83
72
q
p
=
3
2
Maka matriks F =
83
72
b) (i) Diberi
3
2
3
7
5
1
n
m
q
p
F-1
=
23
78
)5(7)8(2
1
=
n
m
3
7
5
1
Maka m = 8 , n = 2
- 6. (ii)
3
2
23
78
5
1
q
p
=
)3(2)2(3
)3)(7()2(8
5
1
=
12
37
5
1
=
5
12
5
37
Maka : p = 5
37
, q = 5
12 )
9.
a) Diberi
23
47
Q =
10
01
Q =
23
47 -1
=
73
42
)3(4)2(7
1
=
73
42
2
1
=
2
7
2
3
21
b)
7p + 4q = 13
3p + 2q = 7
23
47
q
p
=
7
13
q
p
=
73
42
)3(4)2(7
1
7
13
=
)7)(7()13(3
)7)(4()13(2
2
1
=
10
2
2
1
=
5
1
Maka p = 1 , q = 5
- 7. 10.
Diberi P =
32
53
a) Jika PQ = QP = I
32
53
Q =
10
01
Q =
32
53 -1
=
32
53
)2(5)3(3
1
=
32
53
1
1
=
32
53
b) 3s + 5t = 8
2s + 3t = 6
32
53
t
s
=
6
8
t
s
=
32
53
)2(5)3(3
1
6
8
=
)6(3)8(2
)6)(5()8(3
1
1
=
2
6
1
1
=
2
6
Maka s = -6 , t = 2
11.
a)
12
31
R =
10
01
.
R =
12
31 -1
=
12
31
)2(3)1(1
1
=
12
31
5
1
- 8. Diberi
1
311
km
=
12
31
5
1
Maka m = 5 , k = 2
b)
5
5
12
31
y
x
y
x
=
12
31
)2(3)1(1
1
5
5
=
)5(1)5(2
)5)(3()5(1
5
1
=
5
10
5
1
=
1
2
Maka x = 2 , y = 1
12. a) Diberi
10
01
62
7
42
761 s
r
42
761
r
=
42
76 -1
42
761
r
=
ss 2
76
)2)(7()6(
1
42
761
r
=
ss 2
76
146
1
S = 4
Masukkans =4 dalam r = -6s + 14
r = -6 (4) + 14
r = -10
Maka s = 4 , r = -10
b )
6
3
42
76
y
x
y
x
=
62
74
)2(7)4(6
1
6
3
=
)6)(6()3(2
)6)(7()3(4
1424
1
- 9. =
30
30
10
1
=
3
3
Maka x = 3 , y = 3
13.
a)
24
35 -1 =
54
32
)4(3)5(2
1
=
54
32
22
1
Diberi
m
5
32
n
=
54
32
22
1
Maka m = 1/22 n = 4
b)
5x + 3y = 26
-4x + 2y = -12
24
35
y
x
=
12
26
y
x
=
54
32
)4(3)5(2
1
12
26
=
)12(5)26(4
)12)(3()26(2
22
1
=
44
88
22
1
=
2
4
Maka x = 4 , y = 2
- 10. 14.
a)
32
23 -1 =
32
23
)2)(2()3(3
1
=
32
23
5
1
Diberi :
3
231
mR
=
32
23
5
1
Maka R = 5 , m = -2
b)
3x - 2y = 8
2x - 3y = 7
7
8
32
23
y
x
y
x
=
32
23
)2)(2()3(3
1
7
8
=
)7(3)8(2
)7)(2()8(3
5
1
= -
5
10
5
1
=
1
2
Maka x = 2 , y = -1
15.
a) M
23
47
=
10
01
M =
23
47 -1
=
73
42
)3)(4()2(7
1
= -
73
42
2
1
=
2
7
2
3
21
- 11. b)
7x - 4y = -2
3x - 2y = 4
23
47
y
x
=
4
2
y
x
=
73
42
)3)(4()2(7
1
4
2
=
)4)(7()2(3
)4(4)2(2
2
1
=
34
20
2
1
=
17
10
Maka x = -10 , y = -17
16.
a) 5h + 3s = 240
4h + 2s = 176
24
35
s
h
=
176
240
b)
24
35
s
h
=
176
240
s
h
=
54
32
)4)(3()2(5
1
176
240
=
)176)(5()240(4
)176)(3()240(2
2
1
=
80
48
2
1
=
40
24
Maka h = 24 , s = 40
17. a) 8x + 40y = 440
6x + 25y = 290
256
408
y
x
=
290
440
- 12. b)
256
408
y
x
=
290
440
y
x
=
86
4025
)6)(40()25(8
1
290
440
=
)290)(8()440(6
)290)(40()440(25
2
1
=
320
600
40
1
=
8
15
Maka x = 15 , y = 8
18.
a) i) N =
34
1t
ad – bc = 0
3t - 1(4)= 0
t =
4
3
ii)
Diberi t = 2
N =
34
12
N-1 =
24
13
)4)(1()3(2
1
=
24
13
2
1
=
12
2
1
2
3
b)
2x + y = 1
4x + 3y = 5
34
12
y
x
=
5
1
y
x
=
24
13
)4)(1()3(2
1
5
1
=
)5)(2()1(4
)5)(1()1(3
2
1
- 13. =
6
2
2
1
=
3
1
Maka x = -1 , y = 3
19.
Diberi P=
40
03
, Q =
y
x
0
0
PQ = P + Q
40
03
y
x
0
0
=
40
03
+
y
x
0
0
)(4)0)(0()0(4)(0
)(0)0)(3()0(0)(3
yx
yx
=
y
x
400
003
y
x
40
03
=
y
x
40
03
3x =3+x
2X =3
X =
3
2
4y = 4 + y
3y = 4
y =
4
3
Maka X =
3
2
, y =
4
3
20.
n
m
5
3
16
1
35
2n
=
10
01
)3()2(5)5()(5
)3()2(3)5()(3
16
1
nnn
mmn
=
10
01
-6 + 3m = 0