Matematika

Pertanyaan

Determinan matriks B yang memenuhi persamaan  [tex]\left(\begin{array}{ccc}-4& &2\\ & & \\5& &-2\end{array}\right) = B \left(\begin{array}{ccc}9& &-1\\ & & \\-10& &2\end{array}\right) adalah...[/tex]

1 Jawaban

  • sekali lagi angkanya jelek alias pecahan :V[tex]B = \left[\begin{array}{ccc}-4&2\\5&-2\end{array}\right] \frac{1}{18-10} \left[\begin{array}{ccc}2&1\\10&9\end{array}\right] \\ B = \left[\begin{array}{ccc}-4&2\\5&-2\end{array}\right] \frac{1}{8} \left[\begin{array}{ccc}2&1\\10&9\end{array}\right] \\ B = \left[\begin{array}{ccc}-4&2\\5&-2\end{array}\right] \left[\begin{array}{ccc}\frac{2}{8}&\frac{1}{8}\\\frac{10}{8}&\frac{9}{8}\end{array}\right] [/tex]
    [tex]B = \left[\begin{array}{ccc}-4&2\\5&-2\end{array}\right] \left[\begin{array}{ccc}\frac{2}{8}&\frac{1}{8}\\\frac{10}{8}&\frac{9}{8}\end{array}\right] \\ B = \left[\begin{array}{ccc}\frac{-8}{8}+\frac{20}{8}&\frac{-4}{8}+\frac{18}{8}\\\frac{10}{8}-\frac{20}{8}&\frac{5}{8}-\frac{18}{8}\end{array}\right] \\ B = \left[\begin{array}{ccc}\frac{12}{8}&\frac{14}{8}\\\frac{-10}{8}&\frac{-13}{8}\end{array}\right] \\[/tex]
    [tex]B = \left[\begin{array}{ccc}\frac{6}{4}&\frac{7}{4}\\\frac{-10}{8}&\frac{-13}{8}\end{array} \right] [/tex]

    * Determinan
    = (6/4)(-13/8) - (7/4)(-10/8)
    = -78/32 - (-70/32)
    = -78/32 + 70/32
    = -8/32
    = -1/4

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