A 12 A 116 B 13 C 14 D B 12 B 112 C 14 D C 14 A 116

A = 1/2 A + 1/16 B + 1/3 C + 1/4 D B = 1/2 B + 1/12 C + 1/4 D C = 1/4 A + 1/16 B + 1/2 C + 1/4 D D = 1/4 A + 1/8 B + 1/12 C + 1/4 D Solve for A, B, C, D |1/2 0 1/4 1/4 1/16 1/2 1/16 1/8 1/3 1/12 1/2 1/12 1/4 1/4 1/4 1/4|

Solution

If we shift A to the right side in equation 1

(-1/2)A+ (1/16)B+(1/3)C+(1/4)D = 0

Similarly second , third, and fourth equations are

0.A+(-1/2)B+(1/12)C+(1/4)D = 0

(1/4)A+(1/16)B-(1/2)C+(1/4)D= 0

(1/4)A+(1/8)B+(1/12)C-(3/4)D = 0

All these four equations have 0 on their right side.

Obvious solution to these set of equations are

A=B=C=D=0 ...........Ans