KUINTRIK...(kuis invers matriks)Tentukan Invers Matriks B pada lampiranjangan lupa sertakan cara pen.... Question from @JavierSKho13

August 2022 1 53 Report

KUINTRIK...
(kuis invers matriks)

Tentukan Invers Matriks B pada lampiran

jangan lupa sertakan cara penyelesaian dan metode yang digunakan.

Terima kasih ^^

ridhovictor4

Jawab:

Penjelasan dengan langkah-langkah:

$\displaystyle \bold{B} = \left[\begin{array}{ccc}2&1&0\\3&4&-5\\-1&3&6\end{array}\right]$

Eliminasi menggunakan Metode Gauss Jordan (BB⁻¹B⁻¹ = IB⁻¹ = B⁻¹) :

- Eliminasi pada B menjadi I :

$\left[\begin{array}{ccc}2&1&0\\3&4&-5\\-1&3&6\end{array}\right] \xrightarrow{ \displaystyle 1)2B_3+B_1\to B_3, 2)\; \frac{2B_2-3B_1}{5}\to B_2, 3)\; \frac{B_3-7B_2}{26}\to B_3 \;}\\ \left[\begin{array}{ccc}2&1&0\\0&1&-2\\0&0&1\end{array}\right]$

$\left[\begin{array}{ccc}2&1&0\\0&1&-2\\0&0&1\end{array}\right]\xrightarrow{ \displaystyle 1)\;B_2+2B_3\to B_2, 2)\; \dfrac{B_1-B_2}{2}\to B_1} \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$

- Eliminasi pada I menjadi B⁻¹ :

$\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] \xrightarrow{ \displaystyle 1)2B_3+B_1\to B_3, 2)\; \frac{2B_2-3B_1}{5}\to B_2, 3)\; \frac{B_3-7B_2}{26}\to B_3 \;}\\ \left[\begin{array}{ccc}1&0&0\\-3/5&2/5&0\\1/5&-7/65&1/13\end{array}\right]$

$\left[\begin{array}{ccc}1&0&0\\-3/5&2/5&0\\1/5&-7/65&1/13\end{array}\right]\xrightarrow{ \displaystyle 1)\;B_2+2B_3\to B_2, 2)\; \dfrac{B_1-B_2}{2}\to B_1} \\\left[\begin{array}{ccc}3/5&-6/65&-1/13\\-1/5&12/65&2/13\\1/5&-7/65&1/13\end{array}\right]$

$\bold{B}^{-1} = \left[\begin{array}{ccc}3/5&-6/65&-1/13\\-1/5&12/65&2/13\\1/5&-7/65&1/13\end{array}\right]$

cek :

$\bold{BB}^{-1} = \left[\begin{array}{ccc}2&1&0\\3&4&-5\\-1&3&6\end{array}\right]\left[\begin{array}{ccc}3/5&-6/65&-1/13\\-1/5&12/65&2/13\\1/5&-7/65&1/13\end{array}\right]\\\bold{BB}^{-1} = \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$