mohon bantuannya kak
1) Bentuk perkalian dari matriks X adalah opsi A.
[tex]X = \left[\begin{array}{cc}-5&8\\2&-3\end{array}\right] \left[\begin{array}{c}4\\5\end{array}\right] [/tex]
2) Matriks X yang memenuhi dari perkalian matriks tersebut adalah opsi C.
[tex]X = \left[\begin{array}{c}\frac{1}{2}\\0\end{array}\right] [/tex]
Penjelasan dengan langkah-langkah
Sifat invers matriks.
- AX = B ⇒ X = A⁻¹B
- XA = B ⇒ X = BA⁻¹
Nomor 1
Diketahui
[tex]\left[\begin{array}{cc}3&8\\2&5\end{array}\right]X = \left[\begin{array}{c}4\\5\end{array}\right] [/tex]
Ditanyakan
Tentukan perkalian dari matriks X!
Jawab
Misal
[tex]B = \left[\begin{array}{c}4\\5\end{array}\right][/tex]
[tex]A = \left[\begin{array}{cc}3&8\\2&5\end{array}\right][/tex]
Invers dari matriks A.
[tex]A^{-1} = \frac{1}{15 - 16}\left[\begin{array}{cc}5&-8\\-2&3\end{array}\right][/tex]
[tex]A^{-1} = \frac{1}{-1}\left[\begin{array}{cc}5&-8\\-2&3\end{array}\right][/tex]
[tex]A^{-1} = \left[\begin{array}{cc}-5&8\\2&-3\end{array}\right][/tex]
Jadi
AX = B
X = A⁻¹B
[tex]X = \left[\begin{array}{cc}-5&8\\2&-3\end{array}\right] \left[\begin{array}{c}4\\5\end{array}\right] [/tex]
Jawaban A
Nomor 2
Diketahui
[tex]\left[\begin{array}{cc}6&10\\4&7\end{array}\right]X = \left[\begin{array}{c}3\\2\end{array}\right] [/tex]
Ditanyakan
Tentukan matriks X yang memenuhi!
Jawab
Misal
[tex]B = \left[\begin{array}{c}3\\2\end{array}\right][/tex]
[tex]A = \left[\begin{array}{cc}6&10\\4&7\end{array}\right][/tex]
Invers dari matriks A.
[tex]A^{-1} = \frac{1}{42 - 40}\left[\begin{array}{cc}7&-10\\-4&6\end{array}\right][/tex]
[tex]A^{-1} = \frac{1}{2}\left[\begin{array}{cc}7&-10\\-4&6\end{array}\right][/tex]
Jadi
AX = B
X = A⁻¹B
[tex]X = \frac{1}{2}\left[\begin{array}{cc}7&-10\\-4&6\end{array}\right]\left[\begin{array}{c}3\\2\end{array}\right] [/tex]
[tex]X = \frac{1}{2} \left[\begin{array}{c}21-20\\-12+12\end{array}\right] [/tex]
[tex]X = \frac{1}{2} \left[\begin{array}{c}1\\0\end{array}\right] [/tex]
[tex]X = \left[\begin{array}{c}\frac{1}{2}\\0\end{array}\right] [/tex]
Jawaban C
Pelajari lebih lanjut
Materi tentang matriks brainly.co.id/tugas/51941924
#BelajarBersamaBrainly #SPJ1
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