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If Δ is the value of the determinant

then what is the value of the following determinant?

(p ≠ 0 or 1, q ≠ 0 or 1)

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  1. pΔ
  2. qΔ
  3. (p + q)Δ
  4. pqΔ

Answer (Detailed Solution Below)

Option 4 : pqΔ
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Detailed Solution

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Concept:

Using Scalar Multiple Property:

If all the elements of a row (or column) of a determinant are multiplied by a non-zero constant, then the determinant gets multiplied by the same constant.

Calculation:

Δ = 

Column 1 of all elements is multiplied by p then given matrices is also multiplied by p

pΔ = 

Again, column 3 of all elements is multiplied by q then given matrices is also multiplied by q

pqΔ = 

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