Diketahui matriks A=(4 -2 1 5), B=(3 7 -2 -4), dan C=(7 -9

Invers matriks X adalah [[1/15, 2/15], [2/5, -1/5]].

Pembahasan

Untuk menyelesaikan soal ini, kita perlu melakukan beberapa langkah perhitungan matriks:

1.  **Hitung 2B:**
    2B = 2 * [[3, 7], [-2, -4]] = [[6, 14], [-4, -8]]

2.  **Hitung C^T (transpose matriks C):**
    C = [[7, -9], [10, -2]]
    C^T = [[7, 10], [-9, -2]]

3.  **Hitung X = A + 2B - C^T:**
    X = [[4, -2], [1, 5]] + [[6, 14], [-4, -8]] - [[7, 10], [-9, -2]]
    X = [[4+6-7, -2+14-10], [1+(-4)-(-9), 5+(-8)-(-2)]]
    X = [[3, 2], [6, -1]]

4.  **Cari Invers matriks X (X⁻¹):**
    Untuk matriks 2x2 [[a, b], [c, d]], inversnya adalah (1 / (ad - bc)) * [[d, -b], [-c, a]].
    Di sini, a=3, b=2, c=6, d=-1.
    Determinan (ad - bc) = (3 * -1) - (2 * 6) = -3 - 12 = -15.

    X⁻¹ = (1 / -15) * [[-1, -2], [-6, 3]]
    X⁻¹ = [[-1/-15, -2/-15], [-6/-15, 3/-15]]
    X⁻¹ = [[1/15, 2/15], [6/15, -3/15]]
    X⁻¹ = [[1/15, 2/15], [2/5, -1/5]]

Jadi, invers matriks X adalah [[1/15, 2/15], [2/5, -1/5]].