Let A= [a_ i j ] be a matrix of order 3 3 , with a_ i j =( 2 )^ i+j . If the sum of all the elements in the third row of A^2 is + 2 , , Z , then + is equal to :

Step-by-step solution

aligned & A= [ array lll ( 2 )^2 & ( 2 )^3 & ( 2 )^4 ( 2 )^3 & ( 2 )^4 & ( 2 )^5 ( 2 )^4 & ( 2 )^5 & ( 2 )^6 array ] & A= [ array ccc 2 & 2 2 & 4 2 2 & 4 & 4 2 4 & 4 2 & 8 array ] & A^2=2^2 [ array ccc 1 & 2 & 2 2 & 2 & 2 2 2 & 2 2 & 4 array ] [ array ccc 1 & 2 & 2 2 & 2 & 2 2 2 & 2 2 & 4 array ] aligned =4 [ array ccc - & - & - - & - & - (2+4+8) & (2 2 +4 2 +8 2 ) & (4+8+16) array ] Sum of elements of 3^ nd row =4(14+14 2 +28) aligned & =4(42+14 2 ) & =168+56 2 & + 2 & + =168+56=224 aligned