Matriks X berordo (2×2) yang memenuhi persamaan X = adalah…

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Matriks X berordo (2×2) yang memenuhi persamaan X = adalah…

Jawaban Terkonfirmasi

Xleft[begin{array}{cc}5&1\-1&-2end{array}right]=left[begin{array}{cc}9&9\7&-4end{array}right] \\ X=left[begin{array}{cc}9&9\7&-4end{array}right]left[begin{array}{cc}5&1\-1&-2end{array}right]^{-1} \\ X=left[begin{array}{cc}9&9\7&-4end{array}right]displaystyle frac{1}{-10+1}left[begin{array}{cc}-2&-1\1&5end{array}right] \\ X=-frac{1}{9}left[begin{array}{cc}9&9\7&-4end{array}right]left[begin{array}{cc}-2&-1\1&5end{array}right]

displaystyle X=-frac{1}{9}left[begin{array}{cc}-18+9&-9+45\-14-4&-7-20end{array}right] \\ displaystyle X=-frac{1}{9}left[begin{array}{cc}-9&36\-18&-27end{array}right] \\ X=left[begin{array}{cc}1&-4\2&3end{array}right]

Jawaban Terkonfirmasi

Jika A = left[begin{array}{ccc}5&1\-1&-2\end{array}right]

B= left[begin{array}{ccc}9&9\7&-4\end{array}right]

dan 
x.A=B

x= B. A^{-1} ..pers 1

cari invers matrix A.

A^{-1}= frac{1}{detA} .Adj.A ..pers 2

det A = 5(-2) – 1(-1)
         = -10+1
         = -9

Adj.A= left[begin{array}{ccc}-2&-1\1&5\end{array}right]

pers 2.  A^{-1}= frac{1}{-9} left[begin{array}{ccc}-2&-1\1&5\end{array}right]

pers 1 : x=left[begin{array}{ccc}9&9\7&-4\end{array}right] .frac{1}{-9} left[begin{array}{ccc}-2&-1\1&5\end{array}right]
 
           x=frac{1}{-9} .left[begin{array}{ccc}9&9\7&-4\end{array}right] left[begin{array}{ccc}-2&-1\1&5\end{array}right]

x=frac{1}{-9} .left[begin{array}{ccc}9(-2)+9.1&9(-1)+9.5\ 7(-2)+(-4).1&7(-1)+(-4).5\end{array}right]

x=frac{1}{-9} .left[begin{array}{ccc}-18+9&-9+45\ -14+(-4)&-7+(-20)\end{array}right]

x=frac{1}{-9} .left[begin{array}{ccc}-9&36\ -18&-27\end{array}right]

x=left[begin{array}{ccc} frac{-9}{-9} & frac{36}{-9}\ frac{-18}{-9} & frac{-27}{-9} \end{array}right]

x=left[begin{array}{ccc} 1&-4\ 2&3\end{array}right]