SOAL CERITA DENGAN PENYELESAIAN MATRIKS
Nadia Nur Anggraini (28)
XI IPS 3
SOAL CERITA DENGAN PENYELESAIAN MATRIKS
Contoh soal 1 :
Arman membeli 5 pensil dan 3 penghapus, sedangkan Susi membeli 4 pensil dan 2 penghapus di toko yang sama. Di kasir, Arman membayar Rp 11.500,00 sedangkan Susi membayar Rp 9.000,00. Jika Dodi membeli 6 pensil dan 5 penghapus, berapa ia harus membayar?
Pembahasan :
Dimisalkan harga satuan pensil = x dan harga satuan penghapus = y
Disusun ke dalam sistim persamaan linear dua variabel (SPLDV)
5x + 3y = 11.500
4x + 2y = 9.000
Sistim persamaan di atas dapat dinyatakan dalam bentuk matriks, yakni
= ![\left[\begin{array}{ccc}11.500\\9.000\\\end{array}\right] \left[\begin{array}{ccc}11.500\\9.000\\\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11.500%5C%5C9.000%5C%5C%5Cend%7Barray%7D%5Cright%5D+)
menggunakan cara invers matriks
![\left[\begin{array}{ccc}11.500\\9.000\\\end{array}\right] \left[\begin{array}{ccc}11.500\\9.000\\\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D11.500%5C%5C9.000%5C%5C%5Cend%7Barray%7D%5Cright%5D+)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] =-\frac{1}{2}\left[\begin{array}{ccc}2(11.500)+(-3)(9.000)\\(-4)(11.500)+5(9.000)\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =-\frac{1}{2}\left[\begin{array}{ccc}2(11.500)+(-3)(9.000)\\(-4)(11.500)+5(9.000)\\\end{array}\right]](https://tex.z-dn.net/?f=+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D+%3D-%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%2811.500%29%2B%28-3%29%289.000%29%5C%5C%28-4%29%2811.500%29%2B5%289.000%29%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] =-\frac{1}{2}\left[\begin{array}{ccc}-4.000\\-1.000\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =-\frac{1}{2}\left[\begin{array}{ccc}-4.000\\-1.000\\\end{array}\right]](https://tex.z-dn.net/?f=+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D+%3D-%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4.000%5C%5C-1.000%5C%5C%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.000&\\500&\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] = \left[\begin{array}{ccc}1.000&\\500&\\\end{array}\right]](https://tex.z-dn.net/?f=+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5C%5Cend%7Barray%7D%5Cright%5D+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1.000%26%5C%5C500%26%5C%5C%5Cend%7Barray%7D%5Cright%5D+)
x = 1.000
y = 500
Diperoleh harga satuan pensil Rp 1.000 dan harga satuan penghapus Rp 500
Jadi, Dodi harus membayar [6 x Rp 1.000] + [5 x Rp 500] = Rp 8.500
Disusun ke dalam sistim persamaan linear dua variabel (SPLDV)
5x + 3y = 11.500
4x + 2y = 9.000
Sistim persamaan di atas dapat dinyatakan dalam bentuk matriks, yakni
menggunakan cara invers matriks
x = 1.000
y = 500
Diperoleh harga satuan pensil Rp 1.000 dan harga satuan penghapus Rp 500
Jadi, Dodi harus membayar [6 x Rp 1.000] + [5 x Rp 500] = Rp 8.500
Contoh soal 2 :

DAFTAR PUSTAKA
http://kuncijawaban4.blogspot.com/2017/02/soal-cerita-matriks.htmlhttps://www.academia.edu/8513445/Soal_Penerapan_Matriks
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