Let a,b,c  be positive real numbers. The following system of equations x2a2+y2b2−z2c2=1 , x2a2−y2b2+z2c2=1  and −x2a2+y2b2+z2c2=1  has

Let x2a2=X , y2b2=Y , z2c2=Z  so that the equations becomeX+Y−Z=1X−Y+Z=1−X+Y+Z=1This system can be written as AX=B , whereA=[11−11−11−111]Now A=|11−11−11−111|=|2001−11−111|Operating R1→R1+R2                =2(−1−1)=−4≠0 .∴  Given system has a unique solution.