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Question
Without expanding, evaluate the following determinants:
`|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|`
Solution
`|(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
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