Question

If A = [ 3 4

5 1] and AB = [ 30 57

16 44],

Find the matrix 'B' .

Answer 1

[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]