Jika berordo 2x2, A=[(0 1)(-6 5)] dan I=[(1 0)(0 1)], tentukan determinan matriks (A−2I)(A−3I).

Halo, Valey V. Kakak bantu jawab ya :) Jawabannya adalah 0. Perhatikan penjelasan berikut. 1.) Jika matriks berordo 2x2 misalkan A = [(a b)(c d)] dikalikan dengan skalar k, maka: kA = [(ka kb)(kc kd)] 2.) Jika matriks berordo 2x2 misalkan A = [(a b)(c d)] dan B = [(e f)(g h)] dioperasikan dengan pengurangan, maka: A - B = [(a-e ... b-f)(c-g ... d-h)] 3.) Jika matriks berordo 2x2 misalkan A = [(a b)(c d)] maka det(A) = ad - bc Diketahui: A = [(0 1)(-6 5)] I = [(1 0)(0 1)] Maka: 2I = 2[(1 0)(0 1)] = [(2.1 2.0)(2.0 2.1)] = [(2 0)(0 2)] A − 2I = [(0 1)(-6 5)] − [(2 0)(0 2)] = [(0−2 ... 1−0)(−6−0 ... 5−2)] = [(−2 1)(−6 3)] 3I = 3[(1 0)(0 1)] = [(3.1 3.0)(3.0 3.1)] = [(3 0)(0 3)] A − 3I = [(0 1)(-6 5)] − [(3 0)(0 3)] = [(0−3 ... 1−0)(−6−0 ... 5−3)] = [(−3 1)(−6 2)] Sehingga: (A − 2I) (A − 3I) = [(−2 1)(−6 3)] . [(−3 1)(−6 2)] = [((−2x(−3))+(1x(−6))) ... ((−2x1)+(1x2))] .. [((−6x(−3))+(3x(−6))) ... ((−6x1)+(3x2))] = [(( 6 − 6 ) .... (−2 + 2))] .. [((18−18) ... (−6 + 6))] = [(0 0)(0 0)] Dengan demikian, nilai determinan (A − 2I) (A − 3I) yaitu: det((A − 2I) (A − 3I)) = 0.0 − 0.0 = 0 − 0 = 0 Jadi, det((A − 2I) (A − 3I)) = 0. Semoga membantu ya :)