A= [3 -2] , B=[1 0] dan P= [x 2] [1 0] [0 2] [1 Y] Jika AP=PB maka P invers =.. Tolong di jawab ya...ini materi yg invers matriks. Mak

Mapel       : Matematika Wajib
Kategori   : Matriks
Kelas        : SMA / MA kelas X
Semester : Genap


Pembahasan:
[tex]A= \left[\begin{array}{cc}3&-2\\1&0\end{array}\right] , B=\left[\begin{array}{cc}1&0\\0&2\end{array}\right], P= \left[\begin{array}{cc}x&2\\1&y\end{array}\right][/tex]
AP = PB
[tex]\left[\begin{array}{cc}3&-2\\1&0\end{array}\right]\left[\begin{array}{cc}x&2\\1&y\end{array}\right]=\left[\begin{array}{cc}x&2\\1&y\end{array}\right]\left[\begin{array}{cc}1&0\\0&2\end{array}\right][/tex]

Nilai x dan y didapati adalah:
x = 1

6 - 2y = 4
    -2y = 4 - 6
    -2y = -2
        y = 1

Maka matriks P adalah:
[tex]P= \left[\begin{array}{cc}1&2\\1&1\end{array}\right][/tex]

Invers P:
[tex]P^-^1= \frac{1}{(-1)}\left[\begin{array}{cc}1&-2\\-1&1\end{array}\right][/tex]
[tex]P^-^1= -1\left[\begin{array}{cc}1&-2\\-1&1\end{array}\right][/tex]
[tex]P^-^1=\left[\begin{array}{cc}-1&2\\1&-1\end{array}\right][/tex]