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Question
Let ∆ = `|("A"x, x^2, 1),("B"y, y^2, 1),("C"z, z^2, 1)|`and ∆1 = `|("A", "B", "C"),(x, y, z),(zy, zx, xy)|`, then ______.
Options
∆1 = – ∆
∆ ≠ ∆1
∆ – ∆1 = 0
None of these
Solution
Let ∆ = `|("A"x, x^2, 1),("B"y, y^2, 1),("C"z, z^2, 1)|`and ∆1 = `|("A", "B", "C"),(x, y, z),(zy, zx, xy)|`, then ∆ – ∆1 = 0.
Explanation:
∆1 = `|("A", "B", "C"),(x, y, z),(zy, zx, xy)|`
= `|("A", x, yz),("B", y, zx),("C", z, xy)|`
= `1/(xyz) |("A"x, x^2, xyz),("B"y, y^2, xyz),("C"z, z^2, xyz)|`
= `(xyz)/(xyz)|("A"x, x^2, 1),("B"y, y^2, 1),("C"z, z^2, 1)|`
= ∆
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