Adik-adik.. apa yang kalian bayangkan ketika mendengar kata matriks? Kalian keinget sama sebuah film berjudul "the matriks" ya? hehe... tapi hari ini, kita mau belajar matriks bukan yang di film itu. Yuk... dicek contoh soal di bawah ini:
Oh iya, mulai sekarang kalian bisa belajar bareng ajar hitung lewat media video lho... materi ini juga bisa kalian lihat di chanel youtube ajar hitung ya.. silahkan klik link video di bawah ini ya jika kalian tertarik...
1. Diketahui matriks
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVlw3_e3SSZ3k83BjBNkfrbmo4AxsAHw5ZqsksEW_h22Y3DWFFX-5BeOHDWdY0_cyTe0xDamk-BVncvhoeaedsZbMaI2xobUh_umy7Qo3OgwOfa8YpUldPnFd2oA99duH7YF9bD5yoZPA/s1600/a.png)
a. -7
b. -5
c. 2
d. 3
e. 12
Pembahasan:
Det (AB – C) = (12.1) – (9.1) = 12 – 9 = 3
Jawaban: D
2. Diketahui matriks
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiAkK28MAuMqWFtngpb_eKO9ZAS-LOaabAJOdFTlEffcnQvUpq_Uc0PAIDhFI3A37DathtBxvQ9_oXOZC8-T1hLQFT0JF5N8TGlzXW3PfNfCDTMiiPxDMwYhAqAyrzg0rHz_Q692ZjcjM/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYhPz9X8RwTYa1pPOkGeIGRJHqfDgCs8smBFzjxXbkf1xUsVIOhPLlC1Ghd7fK6t_3DeJNd3zkdsERzxAOAib8GQqUBsuTI6a59mtoLs6gOrMagEQXm91InbneQi1aCUQbGqBoFFheMFQ/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT_2W2aBy1XKUERwk2sAZYnrCiACk5YnyFdkKV1qhNbDk60cJ2GsiunPkuG04xQHZ-WuE-_-XrXy7X_CyBacN6z7RJm2J5CnogS7WzVWrcHb-ubsV-O0ug18EAMC__j5L5RH49QCzt7Ns/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAOHKyA3AzrECLb5PNyE59mWajK106A4PZHCRRXlo1XaXySBPn39YKEmGtGaKBUS5Y6G9znkS3NosjBJBLCklZI7gwkrts8mPcgMmLmrxFEOGO-EPkKmdCmpNah9-Y_S6K85Z0AEsVLvI/s1600/a.png)
Jawaban: A
3. Matriks X yang memenuhi:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi75lSgoEoYNx0G1LSNr7pal7jUeo9hBHFH7qo089Gp2sYD3EAl-zLd288m7k1VPFwj8QSMKbvWBCYNHBHbGYxxBP-aL7jeWIyLbikNJz3FnBe0LXRx9KFkST216aNJAar7Euk7Oa1wqTQ/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEheU7is4ZxvINd2Vm8CnfZgbHUzkCjoKHALDZIL5IGrwzJRI5j3l0ZjGEYcpD8G6iSIKkbpkjPN89Cio4-QYu-Sr6tN7BjrF9OKEaqUaiZk6i_2PXTyC2rqRz2yh6EVrTih4UUF6BoLO_A/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjge68XjUI5kGTGGada92_u-XhZIfQUgTUdmSVjuIIP6wfry8OSTjhLMHbbz1szIHXLL4M_SC3gsaWhu1He_Fu-qnnbYRzFsIWWLWqXfsjgVesF2kJZsXMb_CHZvDMVrap72fs86Vxfwoc/s1600/a.png)
Jawaban: C
4. Jika
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEihvE4a_abed9SxK6Ck9shwcfk8x1QgT4iH51qH262gfLR8gC7ltwix6ZaeCEfaNMBO63Os-qmWN2GbIqQwniePA8T7i9jCiqYt-1GFPym1jkG4nlX0uvdGDXa9aW-xswf6E4k8drXjQM0/s1600/a.png)
a. -8
b. -6
c. -2
d. 6
e. 8
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnEo5motojPQrR9FwomA9funj-pnN-S4iTkA5fKWGyoO_YnRZf7amOj2NQvSDJqdeP9uqXYqxNhn3Cnvgie7vwtAinvza-6N772aA_aS_zYACYaF2UcB_hNuZ7Z8b_XqvIWPauONCHY9Q/s1600/a.png)
Det(AB + C) = (3.14) – (8.6) = 42 – 48 = -6
Jawaban: B
5. Diketahui matriks:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8g2keweJlLKP0BvYdJj3y14cObOWehU3Zja4yLWXhNOIk64bvBZdKpdTzg7PugQxzKvsLGIGo4TmJ7ol5Uu4N7F8tGdopAgHC07dFlT1WqwJKqHk0QbnU2XWiW44CIJOotlC5t30fT0Y/s1600/a.png)
Nilai x + y adalah ...
a. 2
b. 6
c. 8
d. 10
e. 12
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEggh5VcwUfg4u-9ALB-LVk-QYsEhAwwzJZ0EZDLoX9_gmagYeaj-rGY_C4VB6puWxIOcgubwa_DLasywUpAIwYOYOQLKALKOnfpzfkyBmQZB6xxB9HkHXGhp5lZsgD1jMmySGI1TKQ7-aw/s1600/a.png)
2x – 2 = 10
2x = 12
x = 6
9 – 2y = 5
-2y = -4
y = 2
Nilai x + y = 6 + 2 = 8
Jawaban: C
6. Matriks A =
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp1a7EvNMxOtpe_9wRjLObSNlZKRvsMzc9MAD_ETg-KuBZdfcUuOlOTjd4OGrpnJoU6jjEO-5YvEl5xS7eCz0N3f10UtsXTjL8vLlBrLBe9v8Q1hhJwE-xzEVdOT_J3UsC6f32mIbHX1M/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-GZxZ-kO3H-_R2oLMfoF0EOrDHRabZdxCc3Uad5O_sUIh8X8fK2Qt8JGV7qfP9UaDm1E_ALYXgRp0tCHX-u_5kRtqFmeCm7kOryF1rPCkl10modOSsteg2TYnfqgT3OQ5WC10rI2DAAc/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHcVSuL9XVUe9L7fz77zNkR14Zol8I1Z6w_bmIIqtGw0qZlQ256BS-4S9JbIWhIxFqBTjdRYdbQ619OuZFU1LHIqj27E7n_GosbiVqnJXEyGVYRyIXSLY8SK7Brd36igQcr_bgt5CSpmE/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5ymggt8NlIW8-E8IVYYjP1mefga8rkz9-CDvPiPZZlNezoFNXuB16AOykPwchvM-8KuYLQwpmpkhCJa0Rv3jTdhv15AUs4z73N7LI7COWTLskg8Akha0RSo3bQI-wke9YL9lSyn0Gwoc/s1600/a.png)
Pembahasan:
Hubungan matriks A dan B adalah
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEif_CuM7E0gGjcQuJwSxb9upqQtq3UDgKACfVnsRVj_l_Hphz-AdBEfdXxRcSWmhuFZ0MOC8xBHl4nwb3zv9N5juWx4MMfaOXPzCsrlpwpLTUf4nltJZsXA-DK80gQ1ErdEcXxrAcK_Cyo/s1600/a.png)
Sehingga jika C =
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhj2z5dJCTCvq8NxmpzNoJ0DWnY7Kqhi9S8RCyBuaE3UgaIGPXn2xX5SE0ieu-juuGg215z8fptej415EFm9Nlqn8ZGyLfpUi2Ldnm8MxlvRi-veRVJNzydd3o_ZhZeuWn_lEkL29t6Qvs/s1600/a.png)
dan memiliki hubungan yang sama seperti A dan B dengan D, maka matriks D adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitlVWEzxs3R26oYh5c-5TObvSVx7K6G6xicNJQrQLT10Zr3Kzeqb6DaZANVci45J_Xy354YCZIxMVqDqZdjqeeHeai33WKHSCxWPZIA2O5OlTz8sK68_311efHaRlJ8hO_gb9kGsrKEwk/s1600/a.png)
Jadi, nilai C + D =
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhj2z5dJCTCvq8NxmpzNoJ0DWnY7Kqhi9S8RCyBuaE3UgaIGPXn2xX5SE0ieu-juuGg215z8fptej415EFm9Nlqn8ZGyLfpUi2Ldnm8MxlvRi-veRVJNzydd3o_ZhZeuWn_lEkL29t6Qvs/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitlVWEzxs3R26oYh5c-5TObvSVx7K6G6xicNJQrQLT10Zr3Kzeqb6DaZANVci45J_Xy354YCZIxMVqDqZdjqeeHeai33WKHSCxWPZIA2O5OlTz8sK68_311efHaRlJ8hO_gb9kGsrKEwk/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguyPUi9GUJYo5vXzZRii_FH9WS3zZ9LZnLoTqGN8ciKUQdrdnJogt1itPKmEs4FKXj2pcncYqWgMjgzk3W6P7Js_fs22hT9fs8msIlrViKRPZ-22xgE3a81R1GpkTt6pSdita2iSGy2-E/s1600/a.png)
Jawaban: D
7. Jika matriks
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiivqi8sGeW3g32R4mdMChNKB-hBTY5b1nVLepKCHGNbX4hDARrgvI4E4OgpMdlQrCi87Kgo_i_aMsYGHQDzcAegmhyvSWeIiZz-FfwAwcv6bIhGX4NOJRo6sjwo0HLaEJpfz069Wcmr2g/s1600/a.png)
a. -2
b. -1
c. 0
d. 1
e. 2
Pembahasan:
Suatu matriks tidak memiliki invers jika determinan matriks tersebut adalah 0
Det (A) = 0
((2x + 1) 5) – ((6x – 1)3) = 0
10x + 5 – (18x – 3) = 0
10x + 5 – 18x + 3 = 0
-8x + 8 = 0
-8x = -8
x = 1
Jawaban: D
8. At adalah transpose dari A. Jika:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3fvzTFe3tj22ZmSYReRwoqOKyvJrpNNXTZtUYiBzQydZUIM9K7KmSXWvFxeyHjAnbmdgleRHgjzMMTI1uy1RZzR0cH4XCOupxIQfqPDODdzykfL5zFMZMJ07qUpfqOlcHzXJwFK2X14g/s1600/a.png)
a. -196
b. -188
c. 188
d. 196
e. 21
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEia_zqXGjdw9jmzDLykop3u7BoPX0XhiUn0VeeprGg1OVqNqYVeygHpiaXnGs2l5IA_P3bQNwWdmh3qd2H88FuyGhGUKdbOuY6rlJFBOm6mpVgZP54BGEUbXcb2RnqE8Glv7BT5B4LB9wA/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVM7mtO1Bmy3yUZLkjca4Pv9VFxWpMoXFUJXaI_gJ52u2OKmDWG5WmmuVFxSwtE93KjSr1bxkln8YKYBbJoFwbBrzsRwFrYdF5oBu9QAlRHJtX2eCqDXmP4a8Kj9E5Z1afyHeA8nqM5pc/s1600/a.png)
Det(At B) = (10.34) – (12.12) = 340 – 144 = 196
Jawaban: D
9. Diketahui matriks-matriks :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3Qlpnggt9xuz3SoQd65eQOulwRlncctS3oF_upwTtfmJEGWWl3l1HJAXjkXWtHBfwjTAtTlmvuGd0dD6_kOa4qexyM_59skAycYlLUgTBCjBBjqZ_zFGSz7OmUUeCyjkKowz9EGqUtg0/s1600/a.png)
a. -66
b. -98
c. 80
d. 85
e. 98
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnosfPexqjq8vmEO2qxWiCsxEK1mJK1wvNFyUopENAx1SvEbejXhcFlY-4kpEuOmUoyldizzsXtUX3uuGHxfzgEOvHQiYkcJKQrI9vceIs6SRChjD82BgGWCOaBnrZz7dhKclq4DPIOuw/s1600/a.png)
Det(C) = (-6.11) – (16.2) = -66 – 32 = -98
Jawaban: B
10. Jika M adalah matriks sehingga:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-WifC40jxUQXgwC-2Y_mHBLkrEyRUqON66UXvdD79zjUn-UxjNYpXrzLgBB0o30hFuVWQaAVS1OfFylt5EpAvHZCIFtKd0IqoYS6Imvcbrjr-s1nLse64aeNKWPpPtKp-wfq-RdWnUrE/s1600/a.png)
a. -2
b. -1
c. 0
d. 1
e. 2
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKg0G6QiLRv0qrcYquw6HdPcSlgPQS58F5A3NAOngFy1P2vYPanWTvu2sZqE82YXD1ITR7BLXfVULZdRTJjWoX3bJEThdSLK0opbTuU_AhFmYqsktH6ilPtMTj6VIYeV-Mq30GKgfLxRU/s1600/a.png)
Det(M) = (1.-1) – (0.1) = -1 – 0 = -1
Jawaban: B
11. Jika
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiaSKRAHm5qzPs14AmuXjdoHwXrD9VZ3CJydtZ_XAXLvZ7mjMwgQCxVQzaCQ-wjkEbhVQ2lyY08DWpUlnuQlJK4Z7rfLfnSo_DR2tZ_qoAYFn5xOUKKPHig2q5pkNvNNOASWQHE8ioZYo/s1600/a.png)
a. – 15/4
b. – 9/4
c. 9/4
d. 15/4
e. 5/4
Pembahasan:
3x – 2 = 7
3x = 9
x = 3
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWMoASvhfVGVFDOFcssDpkBwQmBRXqF9EmG1tbxq4PKZgt4MWbvspFJe2qgtktStwe1HURDw4XoUFPpRDPvDOpMlal44w-oQt8EylQshTGWEmyzELccFPxtPSKLWURosi6O8A-cA4Uv9o/s1600/a.png)
2x + 4y = 3
2 (3) + 4y = 3
6 + 4y = 3
4y = -3
y = - ¾
maka x + y = 3 – ¾ = 12/4 – ¾ = 9/4
Jawaban: C
12. Diketahui matriks
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjpOVHUPzi-wCLoCqfp1k76snS5kxTXx1DHe97xck1TAihsmO5I6cGU0m3guA5tKBiyDzxZWaIAgLv-QtWdWXvfXk7jTtO5XBWcMrRWFy_58e0CD14-SlqiX_MVhAqyz_YnVOAOWMwkS7I/s1600/a.png)
a. 8
b. 12
c. 18
d. 20
e. 22
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibQAia7za35DoOFlVTYEkuuMLjf9gAV2OKXgPdNBji-fetvRvveSU1m1NNtcd89F7guJio_YsDkT0B6a8OGX-wyRmVrLyUKO3RxN3B0e8k63irdjIoiQn-RDAXoU5RiRFGK8RT7u3BNBA/s1600/a.png)
3 + x +3 = 8
6 + x = 8
x = 2
5 – 3 – y = -x
2 – y = -2
-y = -4
y = 4
maka nilai x + 2xy + y = 2 + 2.2.4 + 4 = 2 + 16 + 4 = 22
Jawaban: E
13. Jika
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl7d1RIb2lm6yFOOuqWkECICbWm7CJaTZJu2TQOLgtd_J1yXzRGGmDz73zkvgUB43O4qtkNaCUqK8Pfr0mkxojGd_h1ivocs01eFjorhjHFLrH_Qxulus6akvzbE2zQXMZDZ0xcViGi74/s1600/a.png)
a. -2
b. -1
c. 0
d. 1
e. 2
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwsPmh-xqBCryBs9wZeEweIB0EIaZzXYaFpzBOnmkt7NEOhe4orik7Ut1AMAuWbABVCFKRJ8n9YlkhiQW0wOI5PC4i_wxmBWJSM6pH-d5pOVK6aJmiuAbKbXHZyz03yKXDfPwD_NA13sQ/s1600/a.png)
x = 1 dan y = 0
Nilai x + y = 1 + 0 = 1
Jawaban: D
14. Nilai p yang memenuhi persamaan matriks
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTmVM_WltkUals3-prqDfZGkgMLLpHNYw6Vs_Gjy9ZGILkLEp-MvOYW2ovyTTHt0jmdWoRaDJgY_e_96P5OZtlWfquFGD0XMumPsnvlSgRts84ijc8LGULojA_7pchyphenhyphenJ4eMBuQzBckbiU/s1600/a.png)
a. -2
b. -1
c. 0
d. 1
e. 2
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXp9ANYhy5PRZvfKChuOAiIwb6lYiN6DYuvhLN_J6i2IQOD-s2JZKqSmrwwrE_7kd4EALKObjN6BIiNP8uhnHRWbkQ07RS4Wi_n9kI-3sul93Fo844cUCvLRXRrm12Np_YNeLhyphenhyphen66pJAU/s1600/a.png)
2 + 2p = -2
2p = -4
p = -2
Jawaban: A
15. Persamaan garis g dan garis h berturut-turut adalah
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHEY6crK7N8x4gCUDdyF4ECSCNpBlC0q10XHtB6qV4PIleDGRt8ncttoNa2Vrs1BB9F0gftK4V9W54IQhgTTPyUs52gi6c9nwJOKBgfrl8KaMUevysJ7Hr3OPZByZkdU8svV-hNRXnBQM/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7gTL8Z_KPFPa9C0-slGosStl7nBHaQfds9rThxEmPU9RveOsDtwuVus0OzKevvCIzeZgIMQ9kAYwWWqCONwWm-LZav8A4f4hllDXg5p6ewSTkZFpbqtXJUXN-_dbLh-U7u5CsoNx-8YY/s1600/a.png)
Pembahasan:
Garis g =
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZSIMikDH8q_K0qpD38Hmc5rPVwWAvnE5moTex3_H3hAm1mgZIT28xuGF_BHU1w6uEMWEW5DSCZaR35ad9-gGabygefc-4EPKJRpR-P6hnw5A3OXUsESv3EF2mumnPhawBQbjfK_EPedM/s1600/a.png)
Garis g = y – x = 0 atau –x + y = 0
Garis h =
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhf2lmfF1sLfluezgEzTu0iR-j261OTJKmA1B2mHwnzgDrUlgUqSjwNB4SwKyFTWunBs4Wj3V8kSgLJw3g6SncQYDBuuIIdf87Cfr-Ej9pxWYjXfaWOMNXc3_7midnRNVbx9YHI1WWXihw/s1600/a.png)
Garis h = x + y – 1 = 0 atau x + y = 1
Garis g dan h berpotongan di titik A, maka koordinat titik A adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1lBXiGTkhuICcn8See9BvcRHVsJxUWx_3B8-3bCXkYU-DbFXF4K6q6a7GLNbKWqZFX4lP_FoVAGhnqAMkSEZOaw6efunAa3_5Qf7rU2FJTpVnnX0WxHIGkaCE0unE2cizv4vuGFLMYhs/s1600/a.png)
subtitusikan x = ½ dalam persamaan x + y = 1
x + y = 1
½ + y = 1
y = ½
titik A ( ½ , ½ )
titik B (p, 1) terletak pada g, maka:
–p + 1 = 0
p = 1
titik B (1, 1)
titik C (2, q) terletak pada garis h, maka:
2 + q = 1
q = -1
Titik C (2, -1)
Persamaan garis BC yang melalui titik B (1, 1) dan C (2, -1) adalah:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh0kp-RysGqF5zGeJOSEl-EfnMBHPlShL7OrMHKjYiyUlPlltddT98mvZJHxq_xITHaVX6_MPI2HiMyHb_7AwVDMv6f-Aif0UIzPl4ogg1PWyrdYhl9feWHFps5WqF96f0QFeLYRMd2Ecw/s1600/a.png)
y – 1 = -2x + 2
2x + y = 3 atau y = – 2x + 3, maka gradien garis BC = -2
Maka, persamaan garis k adalah (m = -2 (karena sejajar dengan BC, melalui titik A ( ½ , ½ ) :
y – y1 = m (x – x1)
y – ½ = -2 (x – ½ )
y = -2x + 1 + ½
y = -2x + 1 1/2
Jawaban: E
16. jika
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKH81QNCTv22C9piu4a75wnPMqkdhyphenhyphens06jBncRuUU5h2Hfnj1QSG-Ntf5QgVahXYtwV6Y9Gj3tETcZVn7KoOfZlv0uYDb08smgmXrp4mfOr6QD9IxoPvOZyvwqTQBp3PS6m3na9DuFrNo/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAw9T34ukLmeayAqCA66NHJJjOziw5hygAlnFnpNBvnho1o77FGbWyv5xM65eztx7Tu2MIy6fmrNljJpoFyv96CH5uK5hcbvC4JaIT6npwJ6UDj3E3Uw3k85_FPbJDCsd78GCh1hGqP04/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKH81QNCTv22C9piu4a75wnPMqkdhyphenhyphens06jBncRuUU5h2Hfnj1QSG-Ntf5QgVahXYtwV6Y9Gj3tETcZVn7KoOfZlv0uYDb08smgmXrp4mfOr6QD9IxoPvOZyvwqTQBp3PS6m3na9DuFrNo/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDAvPPC43VCVM99ln3psKOAF-kMARv4ADH7WBDJ-lHtwFuudWVRg2WxYofzrFkESc_XjBoR7DVMmIo6tL77nOFrwoiwDiJcwk75PQHi7j9MMBeWbHjS3HFUgNDb-N-G-FwoKc_7ss-EwE/s320/a.png)
Jawaban: E
17. Jika P dan Q adalah matriks berordo 2 x 2 yang memenuhi
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipv41iyyWUg_hvDnvLTDlWFG3sXvjl5TU0qcHEJSsVjZoR0mPW2XLIqBz7H4RW6DliOJUJPV_0O8SFfOkym1KXd7y1kU3YTSgmo6due9uRFagvLZhr764hhhmMCOFn4wWD7QXH28z7tcI/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiChx3sHvL2AD3ijM_RwC5wOi0qXaXLC2whcW8tUyxmk9xi6essBspepvUzvaQoWrvrm0ZKsoVAnw4xGHsXLXjwKzh1-AqoCNC1F7177yw4ejxHhb6vaSbt9VriaLrxxjm6BKVcg887V_s/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAwisr9GJEqU67Y4ay_tvAAhVfrMvZnywjmy5iQqmZQ8jSsBf_PNTYZJ2qaHavUs4AHS8fR0-FxSoo4LRSkk194beTsyIENjS2aoYtzBIsUr9rIZSgB9RvKqBl86GRnsnYy-njf4Xa7zY/s1600/a.png)
Jawaban: E
18. Jika
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-kdWk0rRGCvqp_tfxjd68weOw_H8XQloMjbnAL5Qqt2yGWBiIcKgc1AnCJarDSI3Uu0JiB7l5M5Myhy1uQ3rXDL2md_WqroA_Awx1UEBzfH28pPYO78wFuHwGVrtbA5jE_nJQU2FN1LQ/s1600/a.png)
a. 3 atau 4
b. -3 atau -4
c. 3 atau -4
d. -4 atau -5
e. 3 atau -5
Pembahasan:
Det(A) = (5 + x) 3x – 5x =
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMGp3cyKodyhS_9JexWMo1PjsbJZhycTJoe4DmaVaJu7n_HkmYLfXn3R0YOtSF9TJP3erJm9c9H6A8rPuLe0b1fvha9-DNGi6Fdk2lFTDefYqBE-Z3_0XGcPPyIQ_PkvYEgIn7ft-fQUU/s1600/a.png)
Det(B) = 9.4 – 7.(-x) = 36 + 7x
Det(A) = det(B)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhguiJcU8VvfkN5rmej3feSVpfvBx2hb58_SNTPvjrrLVV7-knSEzO7Ps2peXj7qrRMm6kc-U4m1vpgoIvKogBAzn3Wa9z9QDDiNxUMKSnG2AOm0RZCnD1Fj_JGLQaY4IS8o8St6xqMSLo/s1600/a.png)
(3x – 9) (x + 4) = 0
x = 3 atau x = -4
Jawaban: C
19. Hasil kali semua nilai x sehingga matriks
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhF81e3f7Lc_mlIKkpdDRpwQFBV9k1WuJ65ss1q2uJqehPcpHRqJysILSATXLtdHpV6vArxH3YzwHZfe5jg7MZ2_TJUQ7ldaBg1c7JEqXDyY2U4S5pcIivW9qByhEyi5p0PZPpG-EIXYY0/s1600/a.png)
a. 20
b. -10
c. 10
d. -20
e. 9
Pembahasan:
Syarat suatu matriks tidak memiliki invers adalah jika determinan = 0, maka:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnOVIfp1VcyHo6HcJfkFAa8QkZYFNGpHBnQDIw8ohOZUyXIY8W_rv0lWTS9P1mPfcXC8uBXGJiHaM69Cp_3eFBG5XLbqLsn5E_roxzFfyWFNjFGB4Zb3cquVY4ptaPqGmzhtg73qDE_IM/s1600/a.png)
x1 . x2 . x3 = -d/a = -20/1 = -20
Jawaban: D
20. Dua garis dalam persamaan matriks:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiasYYu7LZIP_2vudKqtLsCGbl7UKu2hpSQIHyqLzQI4MgRcltE0AbKS4IjnJ0nGDvBHgWcl9pkm6Q_rfu7th4I9XTeuERM5Lfk726kTY278Ng9qnHw-KVWtFkiXdBQwvBI6RFK4mHqIZI/s1600/a.png)
a. -6 : 1
b. -3 : 2
c. 1 : 1
d. 2 : 3
e. 1 : 2
Pembahasan:
Garis g = -2x + ay = 4
Garis h = bx + 3y = 12
mg = 2/a
mh = -b/3
karena g dan h saling tegak lurus, maka mg x mh = -1, maka:
2/a . –b/3 = -1
-2b/3a = -1
2b/3a = 1
3a = 2b
Sehingga a : b= 2 : 3
Jawaban: D
21. Matriks
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqhOkLZbGNFf5zyOPe1E5ZgjsvXvHr3IquAWHJ-QuCprXDE2GuTcEIIFAhdB3Mtq7PNRmav61IHWO2Nwt5yLVu67yvX8XcAI1WAYHsT0GVT3TlvSHvGcgLet_4NpVA5F17fjJgrZCdQw4/s1600/a.png)
a. -1
b. -2
c. 0
d. 1
e. 2
Pembahasan:
A + Bt = C
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixpJhxgOW_owWSiyJr01wqbCLG2wUcFHJOFctRXJGsmbfviSbi6veRjReEs5XxLXO9QGldJq7XHziOlKe4wvAan5xIVaVGUFtKzyHvbrWUBuSjbq1G48fM5gsm2szJtotgtSLRvp_gvac/s1600/a.png)
a = 1
b =1
a+b-c =0
1 + 1 – c = 0
2 – c = 0
c = 2
c + d = 1
2 + d = 1
d = -1
Jawaban: A
22. Jika
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIIifHawdOvSPTLTWZQ0nEqfhyEgPtLkvKaLoSpoJicmuZIQvxTVwZVzuH_Fcle3iaXQl-OVcig-PJJWZhJiibcoSFJJ_iW97rS7FWREFwlFN1Ugro8aza9zwOl30B2ivZb5ti2h6_2kU/s1600/a.png)
a. -5
b. -4
c. 3
d. 4
e. 5
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj3zm0bInvEf-Vi7Jv4Z1mjEkpJIBnBFt95ZcqgfIZhbgL72uZKTLviX9CE4Pw1R1BY7r9TLw31xQv8WG6zoamje3uL128YycHHkHMVoVwy6rAFB6FMW-jpB5oJ17Qug5OOOyAr8DjUwmE/s1600/a.png)
3 + p = 1
p = -2
-1 + q = 0
q = 1
r = 0
5 + s = 1
s = -4
p + q + r + s = -2 + 1 + 0 – 4 = -5
Jawaban: A
23. Diketahui
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqLZ_EMv8lS-h0v4dHrHaYKtn933ahA4iVgj2h5ZmC2SRTEOFS6B8QYVg9w8wgJPmGnl0EBPyLlfhhqDTXES57lxr9_2mQuXwAN2dWWFnolWVf7MIWPtU0ipNgIbbd3DwR8dRojsUmDIQ/s1600/a.png)
a. x – 12y + 25= 0
b. y – 12x + 25= 0
c. x + 12y + 11= 0
d. y – 12x - 11= 0
e. y – 12x + 11= 0
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir2AK4CIsFDZZaKLw4SLdlahmpZVnqzTFdjOS_igQoRW5GRLJdwxOV76Gi6j8DrKWGkL1oXid4GDOgPVp5VccOKyZZrpvx7FPXevhuuwdXc85WqVpCEveqbqYuGBn7yIFEtwjD9OSr_9U/s1600/a.png)
K = det(BC) = (3.4) – (2.0) = 12 – 0 = 12
Kita cari titik A:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBRF9eTEGL8sow-3Sn1L-L7BVFB7yxauUoMGX52u9TkkWx0ouz28ZO_84v4qebccoagTzYt1TFijECJTlWtKMHbtnjobGKNrgdI56_pMaY5NRJbIlqSN6rwzSIg_o1jjpd04Fppuxx6JQ/s1600/a.png)
subtitusikan x = 2 dalam persamaan x + y = 1
x + y = 1
2 + y = 1
y = -1
Titik A (2, -1)
Persamaan garis bergradien k dan melalui titik A adalah:
y – y1 = m (x – x1)
y + 1 = 12 (x – 2)
y + 1 = 12x – 24
y – 12x = -25 atau y – 12x + 25 = 0
Jawaban: B
24. Jika M matriks berordo 2 x 2 dan
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEidxE-fmt06EQUop5A4hWrt86st6ylYSJmArQ4yG0QbYdSsFwtDff2jYPaPB9NjGzpo9oER0NWtYLC-2QGIQ_OoqFnb-wjTyN68h2Hk9qbTQx7Gr_YoWprsuMtp2MZD18lNSSu89eqCiyQ/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMzWiruyUjzYlml_5zN4dHdpnknxS4KpJQKq19tCR-J9Op8VpWSpF4OB-S330mBVFojbvaVo_r9PqVFitZGiHywRG8mggQvdvymYY2maPsYlCtoaO8kOD1Wwo2aoI7dSL78VgLVwa9DNU/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtZeqT7NZJsNpolmvHyE3lKnKQxz3hIZHyGwVY0VkZjKvYJLyC_6_XMWGaqGaW_Ta8xqikKlKb5kXVN9OYYA7qBahFYhb1RNDPYvkB9xjzq-P2KB9YU-W8B2KZUfIrc2payuU70Xip45Y/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0NIv-eXS24XM2POP50KLZi6ZPF8NrqU8u8Fuj0MYRw4bLo6HN2XC19bM2hjNTRYR2FGWZu2nUsgylbcYo11F22wRS92iYOLgwJMlIeIfAY8QnyaMhGxU6_JyChfmAtgWO0tElTkN7WHg/s1600/a.png)
Jawaban: C
25. Jika matriks
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinflxBKQj3aRfNGTztQvtL1uXq7ocL-2wZluejMXwkm6z0oCBB1XQuBcm7uFrcjV4K8IKnXKLwjty-z5XF5v51X_uDc6GoVLxKWMYrdDQn2zCaT7TZ014hk7sRzI5gHfw3bRS4ChHabww/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDaqyKcAwDpRhJ_e305e2N-6-Tyyp_uK2acDU4RgwpVIecqIzGskYfZou-WzIBXG95lKpl2obCojI4MCvu6Ajvq2SwiL9CUmJ8c2sZZ-LThCCsi6aQRcu225ObsKy_0WvR7N818Eah5jE/s1600/a.png)
Pembahasan:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbBddbbpFFsiX9YTqJrLEjhiTfq9RWgUzQ4uNEnMfCnLoS3kI703XrPCejYlTcnqTJycfqVFF7_BZRuDIowy8qCbvQ9ggH3EUKKQ4jLIM9AUKa-u3BcS-eFtk4eoSs22U7bne2g1egvLk/s1600/a.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3oa0u-WEg-U0bprzPq0n4_9wH4UUCIlx1U7OFzomfnCWPaH1IGK4TGXDWsAWw8OOJ4b4Omz8I6kXNygLvrvXoWCt_KG8kNXaokAHsAaAn2wtppPKEMEYJj4jsTEJhsmViR2Cx49D4ma4/s1600/a.png)
Jawaban: E
kalo -5 ≤ 2x ??? gmana min..bingung nihh
ReplyDelete-5/2≤x
DeleteKak no 24 gimana caranya
ReplyDeleteBagaimna nih
ReplyDelete" nilai A dan B yang memenuhi persamaan [a b a b]^-1 = [1 2 2 1]
Kunjungi mathcyber1997.com ya om
ReplyDeleteMasih kurang mengerti, gk ada yg 2 variabel ditambah ma x nya
ReplyDeleteMasih kurang mengerti, gk ada yg 2 variabel ditambah ma x nya
ReplyDeleteMasih kurang mengerti, gk ada yg 2 variabel ditambah ma x nya
ReplyDeleteThanks you kak
ReplyDeleteIni pdf ya mana?
ReplyDeleteMau download gimana?
Terima kasih 🙏🙏
Yang nomer 2 kok itu bisa 9 asalnya dari mana
ReplyDelete