Matematika

Pertanyaan

Diketahui matriks-matriks :

[tex]A=\left[\begin{array}{ccc}1&1\\0&1\end{array}\right] , B = \left[\begin{array}{ccc}1&2\\2&3\end{array}\right] , C = \left[\begin{array}{ccc}2&4\\6&8\end{array}\right][/tex]

Jika F di definisikan sebagai F ( X , Y , Z) = 4X - 2Y + Z

tentukan :
a). F (A,B,C)
b). F ( 2A , 3B , 2C)

1 Jawaban

  • [tex]F(X,Y,Z)=4X-2Y+Z \\ F(A,B,C)=4A-2B+Z \\ =4 \left[\begin{array}{ccc}1&1\\0&1\end{array}\right] -2 \left[\begin{array}{ccc}1&2\\2&3\end{array}\right] +\left[\begin{array}{ccc}2&4\\6&8\end{array}\right] \\ =\left[\begin{array}{ccc}4&4\\0&4\end{array}\right]-\left[\begin{array}{ccc}2&4\\4&6\end{array}\right]+\left[\begin{array}{ccc}2&4\\6&8\end{array}\right] \\ =\left[\begin{array}{ccc}4&4\\2&6\end{array}\right] \\ \\[/tex]

    [tex] F(2A,3B,2C)=4.2A-2.3B+2C \\ =8A-6B+2C \\ =8 \left[\begin{array}{ccc}1&1\\0&1\end{array}\right] -6 \left[\begin{array}{ccc}1&2\\2&3\end{array}\right] +2\left[\begin{array}{ccc}2&4 \\6&8\end{array}\right] \\ =\left[\begin{array}{ccc}8&8\\0&8\end{array}\right] - \left[\begin{array}{ccc}6&12\\12&18\end{array}\right] +\left[\begin{array}{ccc}4&8\\12&16\end{array}\right] \\ =\left[\begin{array}{ccc}6&4\\0&6\end{array}\right] [/tex]

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