Invers dari matriks R=(1 -3 -6 1 1 0 0 2 4) adalah

R^-1 = [[1, 0, 3/2], [-1, 1, -3/2], [1/2, -1/2, 1]]

Pembahasan

Untuk mencari invers dari matriks R=(1 -3 -6 1 1 0 0 2 4), kita perlu melakukan beberapa langkah:

1.  **Hitung Determinan Matriks R (det(R))**:
    det(R) = 1 * (1*4 - 0*2) - (-3) * (1*4 - 0*0) + (-6) * (1*2 - 1*0)
    det(R) = 1 * (4 - 0) + 3 * (4 - 0) - 6 * (2 - 0)
    det(R) = 1 * 4 + 3 * 4 - 6 * 2
    det(R) = 4 + 12 - 12
    det(R) = 4

2.  **Cari Adjoin Matriks R (adj(R))**:
    Adjoin matriks adalah transpose dari matriks kofaktornya.
    Kofaktor:
    C11 = (-1)^(1+1) * det([[1, 0], [2, 4]]) = 1 * (1*4 - 0*2) = 4
    C12 = (-1)^(1+2) * det([[1, 0], [0, 4]]) = -1 * (1*4 - 0*0) = -4
    C13 = (-1)^(1+3) * det([[1, 1], [0, 2]]) = 1 * (1*2 - 1*0) = 2
    C21 = (-1)^(2+1) * det([[-3, -6], [2, 4]]) = -1 * ((-3)*4 - (-6)*2) = -1 * (-12 - (-12)) = -1 * (-12 + 12) = 0
    C22 = (-1)^(2+2) * det([[1, -6], [0, 4]]) = 1 * (1*4 - (-6)*0) = 1 * (4 - 0) = 4
    C23 = (-1)^(2+3) * det([[1, -3], [0, 2]]) = -1 * (1*2 - (-3)*0) = -1 * (2 - 0) = -2
    C31 = (-1)^(3+1) * det([[-3, -6], [1, 0]]) = 1 * ((-3)*0 - (-6)*1) = 1 * (0 - (-6)) = 1 * 6 = 6
    C32 = (-1)^(3+2) * det([[1, -6], [1, 0]]) = -1 * (1*0 - (-6)*1) = -1 * (0 - (-6)) = -1 * 6 = -6
    C33 = (-1)^(3+3) * det([[1, -3], [1, 1]]) = 1 * (1*1 - (-3)*1) = 1 * (1 - (-3)) = 1 * (1 + 3) = 4

    Matriks Kofaktor:
    [[4, -4, 2],
     [0,  4, -2],
     [6, -6,  4]]

    Adjoin Matriks R (Transpose dari Matriks Kofaktor):
    adj(R) = [[4, 0, 6],
              [-4, 4, -6],
              [2, -2, 4]]

3.  **Hitung Invers Matriks R (R^-1)**:
    R^-1 = (1/det(R)) * adj(R)
    R^-1 = (1/4) * [[4, 0, 6],
                   [-4, 4, -6],
                   [2, -2, 4]]
    R^-1 = [[4/4, 0/4, 6/4],
            [-4/4, 4/4, -6/4],
            [2/4, -2/4, 4/4]]
    R^-1 = [[1, 0, 3/2],
            [-1, 1, -3/2],
            [1/2, -1/2, 1]]

Jadi, invers dari matriks R adalah R^-1 = [[1, 0, 3/2], [-1, 1, -3/2], [1/2, -1/2, 1]].