Contoh Soal Matriks Jawaban +Pembahasan
Soal No.2 (UN 2009)
Diketahui matriks A =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2MCIgaGVpZ2h0PSI0NyIgdmlld0JveD0iMCAwIDYwIDQ3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan B =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2OCIgaGVpZ2h0PSIzOSIgdmlld0JveD0iMCAwIDY4IDM5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
.jika A’ adalah transpose matriks A dan AX = B + A’ maka determinan matriks x adalah …
- 46
- 33
- 27
- -33
- -46
PEMBAHASAN :
![mat12](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzNzAiIGhlaWdodD0iMzE3IiB2aWV3Qm94PSIwIDAgMzcwIDMxNyI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : D
Soal No.3 (SNMPTN DASAR 2011)
jika A adalah matriks 2×2 yang memenuhi
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5MyIgaGVpZ2h0PSIzOCIgdmlld0JveD0iMCAwIDkzIDM4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5MiIgaGVpZ2h0PSI0MSIgdmlld0JveD0iMCAwIDkyIDQxIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
maka hasil kali adalah …
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NiIgaGVpZ2h0PSI0NSIgdmlld0JveD0iMCAwIDU2IDQ1Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NyIgaGVpZ2h0PSIzOCIgdmlld0JveD0iMCAwIDU3IDM4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NiIgaGVpZ2h0PSIzOSIgdmlld0JveD0iMCAwIDU2IDM5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1OCIgaGVpZ2h0PSIzOCIgdmlld0JveD0iMCAwIDU4IDM4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NSIgaGVpZ2h0PSI0MiIgdmlld0JveD0iMCAwIDU1IDQyIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
PEMBAHASAN :
![mat13](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0MjgiIGhlaWdodD0iNTY5IiB2aWV3Qm94PSIwIDAgNDI4IDU2OSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : C
Soal No.4 (UN 2009)
Diketahui 3 matriks
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMTkiIGhlaWdodD0iNDEiIHZpZXdCb3g9IjAgMCAzMTkgNDEiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
.Jika A X B
t – C =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1OCIgaGVpZ2h0PSI0MCIgdmlld0JveD0iMCAwIDU4IDQwIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dengan B
t adalah transpose matriks B, maka nilai a dan b masing-masing adalah …
- -1 dan 2
- 1 dan -2
- -1 dan -2
- 2 dan -1
- -2 dan 1
PEMBAHASAN :
![mat14](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0NTMiIGhlaWdodD0iNDQ3IiB2aWV3Qm94PSIwIDAgNDUzIDQ0NyI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : A
Soal No.5 (SBMPTN 2014 DASAR)
Jika P =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NSIgaGVpZ2h0PSIzNyIgdmlld0JveD0iMCAwIDU1IDM3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NyIgaGVpZ2h0PSIzNyIgdmlld0JveD0iMCAwIDY3IDM3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
= 2 P
-1dengan P(-1) menyatakan invers matriks P, maka x+y=….
- 0
- 1
- 2
- 3
- 4
PEMBAHASAN :
![mat15](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyMjIiIGhlaWdodD0iMjEyIiB2aWV3Qm94PSIwIDAgMjIyIDIxMiI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : C
Soal No.6 (UN 2008)
Diketahui matriks P =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NCIgaGVpZ2h0PSIzNyIgdmlld0JveD0iMCAwIDU0IDM3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan Q =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1OSIgaGVpZ2h0PSIzNyIgdmlld0JveD0iMCAwIDU5IDM3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
Jika P
-1 adalah invers matriks P dan Q
-1 adalah invers matrik Q. Maka determinan matriks P
-1Q
-1 adalah…
- 223
- 1
- -1
- -10
- -223
PEMBAHASAN :
![mat16](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0NDQiIGhlaWdodD0iMjM2IiB2aWV3Qm94PSIwIDAgNDQ0IDIzNiI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : B
Soal No.7 (SNMPTN 2010 DASAR)
Jika M adalah matriks sehingga
, maka determinan matriks M adalah ……
- 1
- -1
- 0
- -2
- 2
PEMBAHASAN :
![mat17](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyNjkiIGhlaWdodD0iMTgyIiB2aWV3Qm94PSIwIDAgMjY5IDE4MiI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : A
Soal No.8 (UN 2004)
Diketahui matriks S =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2OSIgaGVpZ2h0PSIzOCIgdmlld0JveD0iMCAwIDY5IDM4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan M =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2OCIgaGVpZ2h0PSI0MiIgdmlld0JveD0iMCAwIDY4IDQyIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
. Jika fungsi f(S+M, S-M) adalah …
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3OSIgaGVpZ2h0PSI0MSIgdmlld0JveD0iMCAwIDc5IDQxIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4MCIgaGVpZ2h0PSI0MiIgdmlld0JveD0iMCAwIDgwIDQyIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3OCIgaGVpZ2h0PSI0MCIgdmlld0JveD0iMCAwIDc4IDQwIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5NCIgaGVpZ2h0PSI0MiIgdmlld0JveD0iMCAwIDk0IDQyIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4NSIgaGVpZ2h0PSIzOSIgdmlld0JveD0iMCAwIDg1IDM5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
PEMBAHASAN :
![mat18](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzNzEiIGhlaWdodD0iNTcyIiB2aWV3Qm94PSIwIDAgMzcxIDU3MiI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : A
Soal No.9 (SNMPTN 2012 DASAR)
Jika A =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NiIgaGVpZ2h0PSI0MCIgdmlld0JveD0iMCAwIDU2IDQwIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
, B =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3MSIgaGVpZ2h0PSIzOCIgdmlld0JveD0iMCAwIDcxIDM4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
, dan det (AB) = 12 maka nilai x adalah …
- -6
- -3
- 0
- 3
- 6
PEMBAHASAN :
![mat19](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxODgiIGhlaWdodD0iMTk5IiB2aWV3Qm94PSIwIDAgMTg4IDE5OSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : B
Soal No.10 (EBTANAS 2003)
Nilai x
2 + 2xy + y
2 yang memenuhi persamaan
![Contoh Soal Matriks](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxOTIiIGhlaWdodD0iNDQiIHZpZXdCb3g9IjAgMCAxOTIgNDQiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
adalah …
- 1
- 3
- 5
- 7
- 9
PEMBAHASAN :
![mat20](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMDciIGhlaWdodD0iMzI0IiB2aWV3Qm94PSIwIDAgMzA3IDMyNCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : A
Soal No.11 (SBMPTN 2014 DASAR)
Jika matriks A =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMDQiIGhlaWdodD0iNDUiIHZpZXdCb3g9IjAgMCAxMDQgNDUiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
, B =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2OSIgaGVpZ2h0PSIzOCIgdmlld0JveD0iMCAwIDY5IDM4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
Dan C =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2NyIgaGVpZ2h0PSI0MSIgdmlld0JveD0iMCAwIDY3IDQxIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
memenuhi A + B = C
t dengan C
t transpos matriks C maka 2x+3y = …
- 3
- 4
- 5
- 6
- 7
PEMBAHASAN :
![mat21](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMjkiIGhlaWdodD0iMjQ3IiB2aWV3Qm94PSIwIDAgMzI5IDI0NyI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : C
Soal No.12 (EBTANAS 2000)
Diketahui A =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4NCIgaGVpZ2h0PSIzNyIgdmlld0JveD0iMCAwIDg0IDM3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
, B =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5MiIgaGVpZ2h0PSI0MCIgdmlld0JveD0iMCAwIDkyIDQwIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan A
2 = xA + yB. Nilai xy =…
- -4
- -1
- – ½
- 1½
- 2
PEMBAHASAN :
![mat22](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1MzciIGhlaWdodD0iNDE4IiB2aWV3Qm94PSIwIDAgNTM3IDQxOCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : B
Soal No.13 (SNMPTN 2014 DASAR)
Jika
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyMDkiIGhlaWdodD0iNDQiIHZpZXdCb3g9IjAgMCAyMDkgNDQiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
dengan b
2 ≠ 2a
2 maka x + y = ….
- -2
- -1
- 0
- 1
- 2
PEMBAHASAN :
![mat23](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMTkiIGhlaWdodD0iMTU5IiB2aWV3Qm94PSIwIDAgMzE5IDE1OSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : C
Soal No.14 (SNMPTN 2012 DASAR)
Jika AB =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1OSIgaGVpZ2h0PSI0MCIgdmlld0JveD0iMCAwIDU5IDQwIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan det (A) =2 maka det (BA
-1) adalah ….
- 8
- 6
- 4
- 2
- 1
PEMBAHASAN :
![mat24](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMTMiIGhlaWdodD0iMjAxIiB2aWV3Qm94PSIwIDAgMzEzIDIwMSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : D
Soal No.15 (SNMPTN 2009 DASAR)
Matriks A =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1OSIgaGVpZ2h0PSI0NCIgdmlld0JveD0iMCAwIDU5IDQ0Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
mempunyai hubungan dengan matriks B =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4MiIgaGVpZ2h0PSIzOSIgdmlld0JveD0iMCAwIDgyIDM5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
. Jika matriks C =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4NSIgaGVpZ2h0PSI0MSIgdmlld0JveD0iMCAwIDg1IDQxIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan matriks D mempunyai hubungan serupa seperti A dengan B maka matriks C + D adalah …..
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NyIgaGVpZ2h0PSIzOSIgdmlld0JveD0iMCAwIDU3IDM5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NiIgaGVpZ2h0PSIzOSIgdmlld0JveD0iMCAwIDU2IDM5Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI4MyIgaGVpZ2h0PSIzNyIgdmlld0JveD0iMCAwIDgzIDM3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2MCIgaGVpZ2h0PSI0MCIgdmlld0JveD0iMCAwIDYwIDQwIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NiIgaGVpZ2h0PSIzOCIgdmlld0JveD0iMCAwIDU2IDM4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
PEMBAHASAN :
![mat25](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3OTciIGhlaWdodD0iMTUzIiB2aWV3Qm94PSIwIDAgNzk3IDE1MyI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : D
Soal No.16 (UM UGM 2004)
Jika I matriks satuan dan matriks A =
![Contoh Soal Matriks](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3MyIgaGVpZ2h0PSI0NCIgdmlld0JveD0iMCAwIDczIDQ0Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
sehingga A
2 = pA + ql maka p+q sama dengan ….
- 15
- 10
- 5
- -5
- 10
PEMBAHASAN :
![mat26](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzNDkiIGhlaWdodD0iMjM5IiB2aWV3Qm94PSIwIDAgMzQ5IDIzOSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Jawaban : D
Soal No.17
Jika diketahui matriks
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMDgiIGhlaWdodD0iNDEiIHZpZXdCb3g9IjAgMCAzMDggNDEiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
Jika P + Q = R’ dan R’ merupakan transpose matriks R, Tentukan nilai x+y!
PEMBAHASAN :
Diketahui:
P + Q = C’
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIyMzQiIGhlaWdodD0iOTIiIHZpZXdCb3g9IjAgMCAyMzQgOTIiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
Maka diperoleh:
- 6 + x = 3, maka x = -3
- 3 + x – y = 8, maka 3 + (-3) – y = 8
y = -8
Sehingga diperoleh x + y = -3 + (-8) = -11
Soal No.18
Diketahui matriks A =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3MSIgaGVpZ2h0PSI0MCIgdmlld0JveD0iMCAwIDcxIDQwIj48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan B =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI2OSIgaGVpZ2h0PSIzOCIgdmlld0JveD0iMCAwIDY5IDM4Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
Tentukan matriks 4AB – BA!
PEMBAHASAN :
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0ODIiIGhlaWdodD0iMTM0IiB2aWV3Qm94PSIwIDAgNDgyIDEzNCI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgZmlsbD0iI2NmZDRkYiIvPjwvc3ZnPg==)
Soal No.19
Matrik P =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI0OCIgaGVpZ2h0PSIzNyIgdmlld0JveD0iMCAwIDQ4IDM3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
dan Q =.
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI3MSIgaGVpZ2h0PSIzNiIgdmlld0JveD0iMCAwIDcxIDM2Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
Matriks (P – kQ) merupakan matriks singular. Tentukan nilai k
PEMBAHASAN :
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMDYiIGhlaWdodD0iNDMiIHZpZXdCb3g9IjAgMCAzMDYgNDMiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
Karena Matris (P-kQ) singular maka determinan matriks tersebut bernilai 0
|P – k.Q|= 0
Maka :
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMDEiIGhlaWdodD0iNDEiIHZpZXdCb3g9IjAgMCAxMDEgNDEiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
(k+1)k = 12
k2 + k = 12
k2 + k – 12 = 0
(k+4)(k-3) = 0
Maka nilai yang memenuhi adalah k = -4 dan k = 3
Soal No.20
Diketahui matriks P =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI5MSIgaGVpZ2h0PSI0NSIgdmlld0JveD0iMCAwIDkxIDQ1Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
Q =
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1MyIgaGVpZ2h0PSI2NyIgdmlld0JveD0iMCAwIDUzIDY3Ij48cmVjdCB3aWR0aD0iMTAwJSIgaGVpZ2h0PSIxMDAlIiBmaWxsPSIjY2ZkNGRiIi8+PC9zdmc+)
, jika nilai deteminannya adalah 4, Tentukan nilai -2x + y – z = 0
PEMBAHASAN :
Menentukan matriks PQ
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSI1NjkiIGhlaWdodD0iNjciIHZpZXdCb3g9IjAgMCA1NjkgNjciPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxOTgiIGhlaWdodD0iNDUiIHZpZXdCb3g9IjAgMCAxOTggNDUiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
Diketahui determinannya = 4, maka:
![](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxNzgiIGhlaWdodD0iNDYiIHZpZXdCb3g9IjAgMCAxNzggNDYiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIGZpbGw9IiNjZmQ0ZGIiLz48L3N2Zz4=)
8(-2x+y+z)-0=4
Maka
-2x+y+z = 0,5
Bagus nih contoh-contoh soal & pembahasannya. 🙂
Sekalian share tulisan saya: “Istilah ‘Matriks’ dalam Matematika berasal dari kata ‘Rahim’ dalam bahasa Latin.”
https://rk-awan.blogspot.com/2019/07/istilah-matrix-berasal-dari-kata-rahim.html