Berikut ini adalah pertanyaan dari yxts pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas
Minta tolong no.2 donggRules : dilarang ngasal/ngarang, dikerjakan menggunakan caranya!
noted : Ini soal Matriks kelas 11 SMA,bukan soal persamaan linear 3 variabel!
noted : Ini soal Matriks kelas 11 SMA,bukan soal persamaan linear 3 variabel!
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![Matriks INversmisal roti coklat = xroti keju = yroti samir = ymatriks koefisien 3x+ y + 2z = 17.000x+ 2y + z = 13.0002x+ 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 - 6det 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 = 3.0001 roti keju = y = 4.0001 roti semir = z = 2.000](https://id-static.z-dn.net/files/df9/7ecf95776ec6d9b6de4baa0cb7543454.jpg)
![Matriks INversmisal roti coklat = xroti keju = yroti samir = ymatriks koefisien 3x+ y + 2z = 17.000x+ 2y + z = 13.0002x+ 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 - 6det 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 = 3.0001 roti keju = y = 4.0001 roti semir = z = 2.000](https://id-static.z-dn.net/files/df9/8e8f6680fe2c09c9153ec14d073a9ec1.jpg)
![Matriks INversmisal roti coklat = xroti keju = yroti samir = ymatriks koefisien 3x+ y + 2z = 17.000x+ 2y + z = 13.0002x+ 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 - 6det 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 = 3.0001 roti keju = y = 4.0001 roti semir = z = 2.000](https://id-static.z-dn.net/files/d3c/0d53443c06702cb8a28fb508a2cb3742.jpg)
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Last Update: Thu, 01 Dec 22