Terdapat dua matriks:
[tex]A=\left(\begin{array}{ccc}2&-3&1\\-4&0&2\end{array}\right)\\B=\left(\begin{array}{cc}1&-5\\-2&4\\3&6\end{array}\right)[/tex]
Hasil dari perkalian skalar dan perkalian matriks: -2AB adalah sebagai berikut:
[tex]\left(\begin{array}{cc}\bf-22&\bf32\\\bf-4&\bf-64\end{array}\right)[/tex] (b)
Penjelasan dengan langkah-langkah
Diketahui:
[tex]A=\left(\begin{array}{ccc}2&-3&1\\-4&0&2\end{array}\right)\\B=\left(\begin{array}{cc}1&-5\\-2&4\\3&6\end{array}\right)[/tex]
Ditanya: -2AB
Jawab:
- Perkalian skalar
[tex]-2A=-2\left(\begin{array}{ccc}2&-3&1\\-4&0&2\end{array}\right)=\left(\begin{array}{ccc}-2\cdot2&-2\cdot(-3)&-2\cdot1\\-2\cdot(-4)&-2\cdot0&-2\cdot2\end{array}\right)=\left(\begin{array}{ccc}-4&6&-2\\8&0&-4\end{array}\right)[/tex]
- Perkalian matriks
[tex]-2AB=\left(\begin{array}{ccc}-4&6&-2\\8&0&-4\end{array}\right)\left(\begin{array}{cc}1&-5\\-2&4\\3&6\end{array}\right)\\=\left(\begin{array}{cc}-4\cdot1+6\cdot(-2)-2\cdot3&-4\cdot(-5)+6\cdot4-2\cdot6\\8\cdot1+0\cdot(-2)-4\cdot3&8\cdot(-5)+0\cdot4-4\cdot6\end{array}\right)\\=\left(\begin{array}{cc}-4-12-6&20+24-12\\8+0-12&-40+0-24\end{array}\right)\\=\left(\begin{array}{cc}-22&32\\-4&-64\end{array}\right)[/tex]
(b)
Pelajari lebih lanjut
Materi tentang Konsep Syarat Perkalian Matriks pada https://brainly.co.id/tugas/7347142
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