SBMPTN Zone : Matriks

Berikut ini adalah kumpulan soal mengenai Matriks tingkat dasar. Jika ada jawaban yang salah, mohon dikoreksi melalui komentar. Terima kasih.

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No. 1

Jika diketahui matriks $A$ memenuhi persamaan $\left(\begin{array}{cc}2& 1\\ 4& 5\end{array}\right)A=\left(\begin{array}{cc}3& 1\\ 3& 2\end{array}\right)\left(\begin{array}{cc}2& 5\\ 1& 3\end{array}\right)$ maka determinan dari $A^{-1}$ adalah

1. $-2$
2. $-\dfrac12$
3. $0$

4. $\dfrac12$
5. $2$

Ganesha Operation

$\begin{array}{rl}\left(\begin{array}{cc}2& 1\\ 4& 5\end{array}\right)A& =\left(\begin{array}{cc}3& 1\\ 3& 2\end{array}\right)\left(\begin{array}{cc}2& 5\\ 1& 3\end{array}\right)\\ \left|\begin{array}{cc}2& 1\\ 4& 5\end{array}\right||A|& =\left|\begin{array}{cc}3& 1\\ 3& 2\end{array}\right|\left|\begin{array}{cc}2& 5\\ 1& 3\end{array}\right|\\ ((2)(5)-(1)(4))|A|& =((3)(2)-(1)(3))((2)(3)-(5)(1))\\ (10-4)|A|& =(6-3)(6-5)\\ 6|A|& =(3)(1)\\ 6|A|& =3\\ |A|& ={\displaystyle \frac{3}{6}}\\ & ={\displaystyle \frac{1}{2}}\end{array}$

$\begin{array}{rl}\left|A^{-1}\right|& ={\displaystyle \frac{1}{|A|}}\\ & ={\displaystyle \frac{1}{{\displaystyle \frac{1}{2}}}}\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 2}}}}\end{array}$

Jadi, determinan dari $A^{-1}$ adalah $2$.
JAWAB: E

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