Rules : dilarang ngasal/ngarang, dikerjakan menggunakan caranya!
noted : Ini soal Matriks kelas 11 SMA,bukan soal persamaan linear 3 variabel!
Jawaban dan penjelasan sudah saya lampirkan pada dua foto di atas yaa..
Semoga membantu!
Matriks INvers
misal roti coklat = x
roti keju = y
roti samir = y
matriks koefisien
3x+ y + 2z = 17.000
x+ 2y + z = 13.000
2x+ y + z = 12.000
[tex]\sf \left[\begin{array}{ccc}3&1&2\\1&2&1\\2&1&1\end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}17.000\\13.000\\12.000\end{array}\right][/tex]
[tex]\sf \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}3&1&2\\1&2&1\\2&1&1\end{array}\right]^{-1} \left[\begin{array}{ccc}17.000\\13.000\\12.000\end{array}\right][/tex]
misalkan
[tex]\sf A = \left[\begin{array}{ccc}3&1&2\\1&2&1\\2&1&1\end{array}\right][/tex]
det A = 3{2(1) - 1(1)} - 1 {1(1)-1(2)}+ 2{1(1)-2(2)}
det A= 3(1) - 1(-1) + 2(-3)
det A = 3 + 1 - 6
det A = 2
[tex]\sf Adj A = \left[\begin{array}{ccc}1&1&-3\\1&-1&-1\\3&-1&5\end{array}\right][/tex]
[tex]\sf A^{-1} = \frac{1}{det \ A} [ adj A][/tex]
maka
[tex]\sf \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =-\frac{1}{2}\left[\begin{array}{ccc}1&1&-3\\1&-1&-1\\-3&-1&5\end{array}\right] \left[\begin{array}{ccc}17.000\\13.000\\12.000\end{array}\right][/tex]
[tex]\sf \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =-\frac{1}{2}\left[\begin{array}{ccc} -6.000\\-8.000\\-4.000\end{array}\right][/tex]
[tex]\sf \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc} 3000\\4.000\\2.000\end{array}\right][/tex]
maka harga
1 roti coklat = x = 3.000
1 roti keju = y = 4.000
1 roti semir = z = 2.000
