jika P = \left[\begin{array}{cc}1&2\\1&3\end\right[begin{array}{cc}x&y\\-z&z] = 2P⁻¹, dengan P⁻¹ men.... Question from @umaycha

August 2018 1 18 Report

jika P = \left[\begin{array}{cc}1&2\\1&3\end\right[begin{array}{cc}x&y\\-z&z] = 2P⁻¹, dengan P⁻¹ menyatakan invers matriks P, maka x + y =

IcukSugiarto $\underline{\mathfrak{"pembahasan\ soal"}}$

$[1]~~Pertama\ inverskan\ "P", sehingga :$

$P = \left[\begin{array}{cc}1&2\\1&3\end{array}\right]$

$maka\ inversnya :$

$P^{-1} = \frac{1}{ad-bc} \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]$

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

$P^{-1} = \frac{1}{3-2} \left[\begin{array}{cc}3&-2\\-1&1\end{array}\right]$

$P^{-1} = \frac{1}{1} \left[\begin{array}{cc}3&-2\\-1&1\end{array}\right]$

$P^{-1} = \left[\begin{array}{cc}3&-2\\-1&1\end{array}\right]$

$\underline{\mathfrak{sehingga\ untuk\ nilai\ dari :}}$

$\left[\begin{array}{cc}x&y\\-z&z\end{array}\right] = 2P^{-1}$

$\left[\begin{array}{cc}x&y\\-z&z\end{array}\right] = 2\left[\begin{array}{cc}3&-2\\-1&1\end{array}\right]$

$\left[\begin{array}{cc}x&y\\-z&z\end{array}\right] = \left[\begin{array}{cc}6&-4\\-2&2\end{array}\right]$

$\underline{\mathfrak{sehingga\ nilai\ dari :}}$

$x=6\\y=-4\\z=2$

$\underline{\mathfrak{sehingga\ jawaban\ dari\ soal\ tersebut :}}\\\\x+y\\=6+(-4)\\=6-4\\=2$

$========================================$

$\mathfrak{catatan :}\\\\ \boxed{ A= \left[\begin{array}{cc}a&b\\c&d\end{array}\right] ~~\Rightarrow~A^{-1} = \frac{1}{ad-bc} \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]}\\\\\mathfrak{Dimana,}~|A| \neq 0$

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