A. Sistem Pertidaksamaan Linear
A. Sistem Pertidaksamaan Linear
A. Sistem Pertidaksamaan Linear
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Contoh 2.21<br />
Tentukan hasil perkalian matriks berikut ini:<br />
⎛3 1⎞<br />
⎛ 3 4 2⎞<br />
⎜ ⎟<br />
2 4<br />
A = ⎜<br />
−1<br />
0 5<br />
⎟ dan B = ⎜ ⎟<br />
⎝ ⎠ ⎜5 −2⎟<br />
⎝ ⎠<br />
Jawab:<br />
A 2 × 3 . B 3 × 2 = C 2 × 2<br />
A . B =<br />
=<br />
=<br />
Contoh 2.22<br />
⎛3 1⎞<br />
⎛ 3 4 2⎞<br />
⎜ ⎟<br />
2 4<br />
⎜<br />
−1<br />
0 5<br />
⎟ ⎜ ⎟<br />
⎝ ⎠ ⎜5 −2⎟<br />
⎝ ⎠<br />
⎛3(3) + 4(2) + 2(5) 3(1) + 4(4) + (2( −2)<br />
⎞<br />
⎜ ⎟<br />
⎝− (3) + 0(2) + 5(5) − (1) + 0(4) + 5( −2)<br />
⎠<br />
⎛27 15⎞<br />
⎜<br />
22 −11<br />
⎟<br />
⎝ ⎠<br />
Diketahui matriks A =<br />
1) a) A 2<br />
b) A 3<br />
2) A 3 + 2A 2 – 3A<br />
Jawab:<br />
1) a) A 2 = A . A<br />
=<br />
=<br />
b) A 3 =<br />
⎛3 2⎞<br />
⎛3 2⎞<br />
⎜<br />
1 5<br />
⎟ ⎜<br />
⎝ ⎠ 1 5<br />
⎟<br />
⎝ ⎠<br />
⎛11 16⎞<br />
⎜<br />
8 27<br />
⎟<br />
⎝ ⎠<br />
⎛3 2⎞<br />
⎜<br />
1 5<br />
⎟.<br />
Tentukanlah:<br />
⎝ ⎠<br />
⎛3 2⎞<br />
⎛11 16⎞<br />
⎜<br />
1 5<br />
⎟ ⎜<br />
⎝ ⎠ 8 27<br />
⎟<br />
⎝ ⎠ =<br />
⎛49 102 ⎞<br />
⎜<br />
51 151<br />
⎟<br />
⎝ ⎠<br />
Catatan<br />
Jika A suatu matriks persegi atau<br />
matriks kuadrat, maka:<br />
A . A = A 2<br />
A . A = A . A 2 = A 3<br />
A= A . A 3 = A 4<br />
...<br />
A . A . A. ... . A = A . A n-1 = A n<br />
Matriks 47
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