Answer:
[2 6; 6 14]
Explanation:
To find matrix B, we can use the equation AB = [30 57; 16 44] and the given matrix A = [3 4; 5 1].
Let's assume matrix B is of the form [a b; c d].
Now, we can set up the following system of equations using the multiplication of matrices:
3a + 4c = 30
3b + 4d = 57
5a + c = 16
5b + d = 44
Now, let's solve these equations to find the values of a, b, c, and d:
From equation 3, we get c = 16 - 5a
Now, substitute this value of c into equation 1:
3a + 4(16 - 5a) = 30
3a + 64 - 20a = 30
64 - 17a = 30
17a = 34
a = 2
Now, using the value of a, we can find b:
5(2) + c = 16
10 + c = 16
c = 6
Now, we have a = 2, b = 6, and c = 6. Let's find d using equation 4:
5b + d = 44
5(6) + d = 44
30 + d = 44
d = 14
So, matrix B is:
B = [2 6; 6 14]