Question

Pelajaran matriks,sma
matriks A =
| 2 3 |
| -1 -2|
matriks B :
| 6 12 |
| -4 -10 |

jika A kuadrat = XA + YB, maka XY =?

Answer 1

A^2 = XA +YB
|1...0| = x |2... 3| + y|6..12|
|0...1| ......| -1..-2|......|-4.-10|
..
hasil operasi a11 --> 2x + 6y = 1   
hasil operasi a22 -->-2x -10y = 1
jumlahkan
-4y = 2
y = -1/2
2x + 6y= 1
2x  + (-3) = 1
2x = 4
x = 2
,
xy = (2)(-1/2) = -1

Answer 2

A² = XA + YB
[2    3] [2  3] = x[2    3] + y[6   12]
[-1  -2] [-1 -2]     [-1  -2]      [-4 -10]
[1  0] = x[2    3] + y[6   12]
[0  1]      [-1  -2]     [-4  -10]
samakan ruas kiri dan kanan:
1 = 2x + 6y   |kali 3|
0 = 3x + 12y |kali 2|
sehingga:
6x + 18y = 3
6x + 24y = 0
____________ _
- 6y = 3
    y = - 1/2
    x = 2
xy = - 1