′ ) −1 X ′Y b = ( X X 300 2700 ⎡5 ⎤ −1 ′ ( X X ) = ⎢300 27000 2700000 ⎥ ⎢⎣27000 2700000 286740000⎥⎦
−1
d. Untuk mendapatkan nilai invers X’X , digunakan cara kofaktor kofaktor dan determinan: determinan: 1. Minor: M 11 =
27000
2700000
2700000 286740000
M 12 =
= 451980000000 M 21 =
300
27000
2700000 286740000
300
27000
27000
2700000
2700000
27000 286740000
M 13 =
= 13122000000 M 22 =
= 13122000000
M 31 =
300
5
27000
27000 286740000
= 81000000
5
27000
300 2700000
27000
27000
2700000
= 81000000 M 23 =
= 704700000
M 32 =
300
5
300
27000
2700000
= 5400000
M 33 =
= 5400000
5
300
300 27000
= 45000
2. Determinan: Diambil dari baris 1: Misalkan Matriks X’X = Matriks A, Maka nilai deteminannya: A = a11 M 11 − a12 M 12 + a13 M 13 atau A = a11 K 11 + a12 K 12 + a13 K 13
dimana K ij = (−1)i = j M ij
= 5(451980000000) + 300(-13122000000) + 27000(81000000) = 510300000000 3. Matriks Kofaktor: = K ij = (−1)i j M ij
3
⎛ 451980000000 - 13122000000 81000000 ⎞ ⎜ ⎟ K ij = ⎜ - 13122000000 704700000 - 5400000 ⎟ ⎜ - 5400000 45000 ⎠⎟ ⎝ 81000000 4. Adjoint A: adj. A = [K ij ]