The system of equations 3 x+2 y+z=6 , 3 x+4 y+3 z=14 and 6 x+10 y+8 z=a , has infinite number of solutions, if a is equal to

Step-by-step solution

Given system of equation is gathered 3 x+2 y+z=6 3 x+4 y+3 z=14 6 x+10 y+8 z=a A= [ array rrr 3 & 2 & 1 3 & 4 & 3 6 & 10 & 8 array ], B= [ array r 6 14 a array ] gathered Here, A= [ array rrr 3 & 2 & 1 3 & 4 & 3 6 & 10 & 8 array ], B= [ array r 6 14 a array ] aligned & C₁₁=(32-30)=2, C₁₂=-(24-18)=-6, & C₁₃=(30-24)=6 & C₂₁=-(16-10)=-6, C₂₂=(24-6)=18, & C₂₃=-(30-12)=-18 & C₃₁=(6-4)=2, C₃₂=-(9-3)=-6, & C₃₃=(12-6)=6 aligned aligned adj A & = [ array lll C₁₁ & C₁₂ & C₁₃ C₂₁ & C₂₂ & C₂₃ C₃₁ & C₃₂ & C₃₃ array ]^ = [ array