Matematika

Pertanyaan

X adalah matriks persegi berordo 2 yang memenuhi X \left[\begin{array}{ccc}1&2\\2&3&\/\end{array}\right] = \left[\begin{array}{ccc}4&8\\5&8\\\end{array}\right] . Matriks X adalah

1 Jawaban

  • [tex]\displaystyle X \left[\begin{array}{cc}1&2\\2&3\\\end{array}\right] =\left[\begin{array}{ccc}4&8\\5&8\\\end{array}\right] \\ X=\left[\begin{array}{ccc}4&8\\5&8\\\end{array}\right]\left[\begin{array}{cc}1&2\\2&3\\\end{array}\right]^{-1} \\ X=\left[\begin{array}{ccc}4&8\\5&8\\\end{array}\right]\frac{1}{3-4}\left[\begin{array}{cc}3&-2\\-2&1\\\end{array}\right] \\ X=-1\left[\begin{array}{ccc}4&8\\5&8\\\end{array}\right]\left[\begin{array}{cc}3&-2\\-2&1\\\end{array}\right][/tex]
    [tex]X=-1\left[\begin{array}{cc}12-16&-8+8\\15-16&-10+8\\\end{array}\right] \\ X=-1\left[\begin{array}{cc}-4&0\\-1&-2\\\end{array}\right] \\ X=\left[\begin{array}{cc}4&0\\1&2\\\end{array}\right][/tex]

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