Without expanding, show that the value of each of the following determinants is zero:

Question

Philoid · Accepted Answer

Multiplying C₁, C₂ and C₃ with z, y and x respectively we get,

Now, taking y, x and z common from R₁, R₂ and R₃ gives,

Applying C₂ → C₂ – C₃ gives,

As, C₁ = C₂, therefore determinant is zero.