Question

Using properties of determinants, prove that

|(1,1,1+3x)(1+3y,1,1)(1,1+3z,1)|=9(3xyz+xy+yz+zx)

Answer 1

(Using C2 → C2 –C1 & C3 →C3 –C1

= 1 x (9yz) + 3x(3z + 9yz + 3y)

(Expanding along R1)

= 9(3xyz + xy + yz + zx) = RHS