Q. 114.4( 36 Votes )

Find the matrix X

Answer :

Given X

From above equation it can be observed that matrix on R.H.S is a 2×3 matrix and that on the L.H.S is also a 2×3 matrix. Therefore, X must be a 2×2 matrix.


Let X


So the equation is given by:





Now equating the corresponding elements of both the matrices we get,


a + 4b = -7, 2a + 5b = -8, 3a + 6b = -9


c + 4d = 2, 2c + 5d = 4, 3c + 6d = 6


Now, a + 4b = -7 a = -4b -7


2a + 5b = -8 2.(-4b -7) + 5b = -8


-8b -14 + 5b = -8


-3b = 6


b = -2


a = -4b -7 a = -4.(-2) -7


a = 1


Now, c + 4d = 2 c = -4d + 2


2c + 5d = 4 2.(-4d + 2) + 5d = 4


-8d + 4 + 5d = 4


-3d = 0


d = 0


c = -4d + 2 c = -4.0 + 2


c = 2


Thus, a = 1, b = -2, c = 2, d = 0.


Hence X becomes


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