Question

Given matrix A = `[(4sin30^@,cos0^@), (cos0^@,4sin30^@)] and B = [(4), (5)]` If AX = B.
 Find the matrix 'X'

Answer 1

Let the matrix X = `[(x), (y)]`

AX = B

`=> [(4sin30^@,cos0^@), (cos0^@,4sin30^@)][(x), (y)] = [(4), (5)]`

`=> [(4(1/2),1), (1,4(1/2))][(x), (y)] = [(4), (5)]`

`=> [(2,1), (1,2)][(x), (y)] = [(4), (5)]`

`=> [(2x+y), (x+2y)] = [(4), (5)]`

`=> 2x + y = 4 .............(1)
x + 2y = 5 .........(2)

Multiplying (1) by 2, we get

4x + 2y = 8 ….(3)

Subtracting (2) from (3), we get

3x = 3

⇒ x = 1

Substituting the value of x in (1), we get

2(1) + y = 4

⇒ 2 + y = 4

⇒ y = 2

Hence, the matrix X = `[(x), (y)] = [(1), (2)]`