Question

Without expanding, evaluate the following determinants:

`|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|`

Answer 1

`|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)| =|(x + y + z, x + y + z, x + y + z),(z, x, y),(1, 1, 1)|`

`"R"_1 = "R"_1 +"R"_2`

= `(x + y + z)|(1, 1, 1),(z, x, y),(1, 1, 1)|` = 0

∵ R₁ = R₃