- Hasil dari [tex]\left[\begin{array}{ccc}2&1\\3&0\\\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}-2&0&2\\3&1&0\\\end{array}\right][/tex] adalah?
- Jika A = [tex]\left[\begin{array}{ccc}0&1&2\\-2&0&3\\\end{array}\right] \\[/tex] dan B = [tex]\left[\begin{array}{ccc}4&2\\1&0\\3&-1\end{array}\right][/tex] maka A x B?
- Jika P = [tex]\left[\begin{array}{ccc}2&0\\1&3\end{array}\right][/tex] dan Q = [tex]\left[\begin{array}{ccc}-1&1\\2&-3\end{array}\right][/tex] maka matrik hasil dari [tex]P^{2} -PQ-QP+Q{^2}[/tex]?
- Hasil dari [tex]\left[\begin{array}{ccc}12&24\\48&36\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}16&32\\-24&-16\\\end{array}\right][/tex]?
Berikut adalah hasil dari operasi perkalian matriks di atas:
- Hasil dari [tex]\left[\begin{array}{ccc}2&1\\3&0\\\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}-2&0&2\\3&1&0\\\end{array}\right][/tex] adalah: [tex]\left[\begin{array}{ccc}-1&1&4\\-6&1&6\end{array}\right][/tex]
- Jika A = [tex]\left[\begin{array}{ccc}0&1&2\\-2&0&3\\\end{array}\right][/tex] dan B = [tex]\left[\begin{array}{ccc}4&2\\1&0\\3&-1\end{array}\right][/tex] maka A x B adalah: [tex]\left[\begin{array}{ccc}11&-1\\1&-7\end{array}\right][/tex]
- Matriks hasil dari [tex]P^2-PQ-QP+Q^2[/tex] adalah: [tex]\left[\begin{array}{ccc}8&-3\\-10&1\end{array}\right][/tex]
- Hasil dari [tex]\left[\begin{array}{ccc}12&24\\48&36\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}16&32\\-24&-16\\\end{array}\right][/tex] adalah: [tex]\left[\begin{array}{ccc}-384&0\\-78&960\end{array}\right][/tex]
Penjelasan dengan langkah-langkah
1. Diketahui:
[tex]\left[\begin{array}{ccc}2&1\\3&0\\\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}-2&0&2\\3&1&0\\\end{array}\right][/tex]
Ditanya: Hasil perkalian matriks 2x2 dengan 2x3?
Jawab:
[tex]\left[\begin{array}{ccc}2&1\\3&0\\\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}-2&0&2\\3&1&0\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}2(-2)+1(3)&2(0)+1(1)&2(2)+1(0)\\3(-2)+0(3)&3(0)+0(1)&3(2)+0(0)\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-4+3&0+1&4+0\\-6+0&0+1&6+0\\\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-1&1&4\\-6&1&6\end{array}\right][/tex]
2. Diketahui:
A = [tex]\left[\begin{array}{ccc}0&1&2\\-2&0&3\end{array}\right][/tex]
B = [tex]\left[\begin{array}{ccc}4&2\\1&0\\3&-1\end{array}\right][/tex]
Ditanya: A x B?
Jawab:
A x B
= [tex]\left[\begin{array}{ccc}0&1&2\\-2&0&3\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}4&2\\1&0\\3&-1\end{array}\right][/tex]
=[tex]\left[\begin{array}{ccc}0(4)+1(1)+2(3)&0(2)+1(0)2(-1)\\-2(4)+0(1)+3(3)&-2(2)+0(0)+3(-1)\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}4+1+6&0+0+(-1)\\-8+0+9&-4+0+(-3)&\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}11&-1\\1&-7\end{array}\right][/tex]
3. Diketahui:
- P = [tex]\left[\begin{array}{ccc}2&0\\1&3\end{array}\right][/tex]
- Q= [tex]\left[\begin{array}{ccc}-1&1\\2&-3\end{array}\right][/tex]
Ditanya: Matriks hasil dari [tex]P^2-PQ-QP+Q^2[/tex]?
Jawab:
Penjelasan lebih lengkap mengenai soal ini dapat dilihat di gambar terlampir.
[tex]P^2-PQ-QP+Q^2[/tex]
= [tex]\\\left[\begin{array}{ccc}4&0\\5&9\end{array}\right] - \left[\begin{array}{ccc}-2&2\\7&10\end{array}\right] - \left[\begin{array}{ccc}1&3\\1&-9\end{array}\right] + \left[\begin{array}{ccc}3&2\\-7&-7\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}4-(-2)-1+3&0-2-3+2\\5-7-1+(-7)&9-10-(-9)+(-7)\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}8&-3\\-10&1\end{array}\right][/tex]
4. Diketahui: [tex]\left[\begin{array}{ccc}12&24\\48&36\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}16&32\\-24&-16\end{array}\right][/tex]
Ditanya: Hasil perkalian?
Jawab:
[tex]\left[\begin{array}{ccc}12&24\\48&36\end{array}\right][/tex] x [tex]\left[\begin{array}{ccc}16&32\\-24&-16\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}12(16)+24(-24)&12(32)+24(-16)\\48(16)+36(-24)&48(32)+36(-16)\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}192+(-576)&384+(-384)\\768+(-864)&1536+(-576)\end{array}\right][/tex]
= [tex]\left[\begin{array}{ccc}-384&0\\-78&960\end{array}\right][/tex]
Pelajari lebih lanjut
Pelajari lebih lanjut tentang hasil perkalian matriks pada https://brainly.co.id/tugas/21442788
#BelajarBersamaBrainly
#SPJ1
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