Consider a system of linear equation in three variablesx,y,z a_1x+b_1y+ c_1z = d_1 , a_2x+ b_2y+c_2z=d_2 ,a_3x + b_3y + c_3z=d_3 The systemscan be expressed by matrix equation [(a_1,b_1,c_1),(a_2,b_2,c_2),(c_1,c_2,c_3)][(x),(y),(z)]=[(d_1),(d_2),(d_3)] if A is non-singular matrix then the solution of above system can be found by X =A^(-1)B, the solution in this case is unique. if A is a singular matrix i.e.then the system will have no unique solution ifno solution (i.e. it is inconsistent) ifWhereAdjA is the adjoint of the matrix A, which is obtained by taking transpose of the matrix obtained by replacing each element of matrix A with corresponding cofactors. Now consider the following matrix. A=[(a,1,0),(1,b,d),(1,b,c)], B=[(a,1,1),(0,d,c),(f,g,h)], U=[(f),(g),(h)], V=[(a^2),(0),(0)], X=[(x),(y),(z)] IfAX=Uhas infinitely many solutions then the equation BX=Uis consistent if