If A= [ array ccc k / 2 & 0 & 0 0 & l / 3 & 0 0 & 0 & m / 4 array ] and A⁻¹= [ array ccc 1 / 2 & 0 & 0 0 & 1 / 3 & 0 0 & 0 & 1 / 4 array ] , then k+l+m=

Step-by-step solution

Given, A= [ array ccc k / 2 & 0 & 0 0 & l / 3 & 0 0 & 0 & m / 4 array ] and A⁻¹= [ array ccc 1 / 2 & 0 & 0 0 & 1 / 3 & 0 0 & 0 & 1 / 4 array ] Since, A A⁻¹=I aligned & [ array ccc k 2 & 0 & 0 0 & l 3 & 0 0 & 0 & m 4 array ] [ array lll 1 2 & 0 & 0 0 & 1 3 & 0 0 & 0 & 1 4 array ]= [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] & [ array ccc k 4 & 0 & 0 0 & l 9 & 0 0 & 0 & m 16 array ]= [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] aligned On comparing, we get aligned & & k 4 & =1, l 9 =1 and m 16 =1 & & k & =