Question

tolong dibantu!!!!!1 ❗❗❗❓❓❓.sdnmmmcvbmmcvmbmcvbmmc

Answer 1

Jawaban:

1. Untuk menghitung hasil dari operasi matriks yang diberikan, kita akan menggunakan operasi matriks standar:

a. B + C:

```

B + C = [[5, -1], [-2, 6]] + [[1, 2], [7, -8]] = [[6, 1], [5, -2]]

```

b. AB:

```

AB = [[1, 2], [4, 3]] * [[5, -1], [-2, 6]] = [[1*5 + 2*(-2), 1*(-1) + 2*6], [4*5 + 3*(-2), 4*(-1) + 3*6]] = [[1, 11], [14, 10]]

```

c. AC:

```

AC = [[1, 2], [4, 3]] * [[1, 2], [7, -8]] = [[1*1 + 2*7, 1*2 + 2*(-8)], [4*1 + 3*7, 4*2 + 3*(-8)]] = [[15, -14], [25, -16]]

```

d. A(B + C):

```

A(B + C) = [[1, 2], [4, 3]] * [[6, 1], [5, -2]] = [[1*6 + 2*5, 1*1 + 2*(-2)], [4*6 + 3*5, 4*1 + 3*(-2)]] = [[16, 0], [34, 10]]

```

e. AB + AC:

```

AB + AC = [[1, 11], [14, 10]] + [[15, -14], [25, -16]] = [[16, -3], [39, -6]]

```

2. Untuk matriks K, L, dan α yang telah diberikan:

a. KL:

```

KL = [[6, -4], [3, 5]] * [[-2, 8], [10, 3]] = [[6*(-2) + (-4)*10, 6*8 + (-4)*3], [3*(-2) + 5*10, 3*8 + 5*3]] = [[-52, 42], [28, 49]]

```

b. LM:

```

LM = [[-2, 8], [10, 3]] * [[6, -4], [3, 5]] = [[-2*6 + 8*3, -2*(-4) + 8*5], [10*6 + 3*3, 10*(-4) + 3*5]] = [[12, 46], [63, -10]]

```

c. (KL)M:

```

(KL)M = [[-52, 42], [28, 49]] * [[6, -4], [3, 5]] = [[-52*6 + 42*3, -52*(-4) + 42*5], [28*6 + 49*3, 28*(-4) + 49*5]] = [[-348, 320], [252, 315]]

```

d. K(LM):

```

K(LM) = [[6, -4], [3, 5]] * [[12, 46], [63, -10]] = [[6*12 + (-4)*63, 6*46 + (-4)*(-10)], [3*12 + 5*63, 3*46 + 5*(-10)]] = [[-396, 304], [291, 168]]

```

3. Untuk matriks A dan B yang diberikan:

a. (AB):

```

(AB) = [[3, -1], [2, 5]] * [[-1, 3], [7, 1]] = [[3*(-1) + (-1)*7, 3*3 + (-1)*1], [2*(-1) + 5*7, 2*3 + 5*1]] = [[-10, 8], [33, 11]]

```

b. BA¹:

```

BA¹ = [[-1, 3], [7, 1]] * [[3, -1], [2, 5]] = [[(-1)*3 + 3*2, (-1)*(-1) + 3*5], [7*3 + 1*2, 7*(-1) + 1*5]] = [[3, 14], [23, 2]]

```