Exercise Zone : Invers Matriks

Berikut ini adalah kumpulan soal mengenai Invers Matriks. Jika ingin bertanya soal, silahkan gabung ke grup Telegram, Signal, Discord, atau WhatsApp.

Tipe:

Standar SBMPTN HOTS

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No. 1

Jika {P=$$\left(\begin{array}{cc}1& 2\\ 1& 3\end{array}\right)$$} dan {$$\left(\begin{array}{cc}x& y\\ -z& z\end{array}\right)$$=2P^{-1}} dengan P^{-1} menyatakan invers matriks P, maka {x+y=} ....

$$\begin{array}{rl}|P|& =(1)(3)-(2)(1)\\ & =1\end{array}$$

$$\begin{array}{rl}{P}^{-1}& ={\displaystyle \frac{1}{|P|}}\left(\begin{array}{cc}3& -2\\ -1& 1\end{array}\right)\\ & ={\displaystyle \frac{1}{1}}\left(\begin{array}{cc}3& -2\\ -1& 1\end{array}\right)\\ & =\left(\begin{array}{cc}3& -2\\ -1& 1\end{array}\right)\end{array}$$

$$\begin{array}{rl}\left(\begin{array}{cc}x& y\\ -z& z\end{array}\right)& =2P^{-1}\\ \left(\begin{array}{cc}x& y\\ -z& z\end{array}\right)& =2\left(\begin{array}{cc}3& -2\\ -1& 1\end{array}\right)\\ \left(\begin{array}{cc}x& y\\ -z& z\end{array}\right)& =\left(\begin{array}{cc}6& -4\\ -2& 2\end{array}\right)\end{array}$$
x=6 dan y=-4

$$\begin{array}{rl}x+y& =6+(-4)\\ & =2\end{array}$$

Jadi, x+y=2.

No. 2

Jika matriks A=$$\left(\begin{array}{cc}3& -2\\ 7& -5\end{array}\right)$$, invers matriks A adalah A^{-1}= ....

$$\begin{array}{rl}detA& =\left|\begin{array}{cc}3& -2\\ 7& -5\end{array}\right|\\ & =3\cdot (-5)-(-2)\cdot 7\\ & =-15+14\\ & =-1\end{array}$$

$$\begin{array}{rl}{A}^{-1}& ={\displaystyle \frac{1}{detA}}\left(\begin{array}{cc}-5& 2\\ -7& 3\end{array}\right)\\ & ={\displaystyle \frac{1}{-1}}\left(\begin{array}{cc}-5& 2\\ -7& 3\end{array}\right)\\ & =\boxed{{\displaystyle \boxed{{\displaystyle \left(\begin{array}{cc}5& -2\\ 7& -3\end{array}\right)}}}}\end{array}$$

Jadi, A^{-1}=$$\left(\begin{array}{cc}5& -2\\ 7& -3\end{array}\right)$$.