Solve X 2 1 5 2XSolutionLet order of X be m x n Then order

Solution

Let order of X be (m x n). Then, order wise, the given equation is: (n x m) = (2 x 2)(m x n). Applying the condition for matrix multiplication, m = 2 and (n x m) = (2, 2) => m = 2 and n = 2.

Let X = (a b)

(c d)

Then, the given equation becomes:

2a - c = a or a = c....... (1);

2b - d = c ..... ..............(2);

5a - 2c = b or 3c = b ... (3) [since from (1), 5a = 5c] ;

5b - 2d = d or 5b = 3d or 3d = 15c or d = 5c ...... (4) [since from (3), 5b = 15c]

Thus, the matrix X = k(1 3)

   (1 5)

where k is any arbitrary value for c.