A. Sistem Pertidaksamaan Linear
A. Sistem Pertidaksamaan Linear
A. Sistem Pertidaksamaan Linear
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c 21 = (–1) 2+1<br />
M 21 = – M 21 = –13<br />
c = (–1) 22 2+2 M 22 = + M 22 = 3<br />
c 23 = (–1) 2+3<br />
c 31 = (–1) 3+1<br />
c 32 = (–1) 3+2<br />
c 33 = (–1) 3+3<br />
3. Adjoin<br />
M 23 = – M 23 = 17<br />
M 31 = + M 31 = –3<br />
M 32 = – M 32 = 4<br />
M 33 = + M 33 = –6<br />
⎛c11 c21 c31<br />
⎞ ⎛−14 −13 −3⎞<br />
⎜ ⎟ ⎜ ⎟<br />
c<br />
adj A = ⎜ 12 c22 c32<br />
⎟ = ⎜<br />
−10<br />
3 4<br />
⎟<br />
⎜c13 c23 c ⎟ ⎜<br />
⎝ 33 ⎠ 15 17 −6⎟<br />
⎝ ⎠<br />
4. Invers Matriks Ordo 3 × 3<br />
Jika A =<br />
A –1 =<br />
Contoh 2.31<br />
⎛a a a ⎞<br />
11 12 13<br />
⎜ ⎟<br />
⎜<br />
a21 a22 a23<br />
⎟<br />
⎜a31 a32 a ⎟<br />
33<br />
⎝ ⎠<br />
1<br />
det A<br />
. adj A<br />
Carilah invers matriks A =<br />
Jawab:<br />
det A =<br />
2 3 1 2 3<br />
0 −3 −2 0 −3<br />
5 −1 4 5 −1<br />
dan det A ≠ 0, maka invers A adalah:<br />
⎛2 3 1⎞<br />
⎜ ⎟<br />
⎜<br />
0 −3 −2<br />
⎟!<br />
⎜5 −1<br />
4⎟<br />
⎝ ⎠<br />
= (2)(–3)(4) + (3)(–2)(5) + (1)(0)(–1) – (1)(–3)(5) – (2)(–2)(–1) –<br />
(3)(0)(4)<br />
= –24 – 30 – 0 + 15 – 4 – 0<br />
= –43<br />
Matriks 61
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