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

Answer 1

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)|`

= ∆