The value of \(\left| {\begin{array}{*{20}{c}} 1&1&1\\ 1&{1 + {\rm{x}}}&1\\ 1&1&{1 + {\rm{y}}} \end{array}} \right|\) is

Question

Question

This question was previously asked in

NDA (Held On: 19 Apr 2015) Maths Previous Year paper

Attempt Online

Answer 1

Concept:

Elementary row or column transformations do not change the value of the determinant of a matrix.

Calculation:

\(\left| {\begin{array}{*{20}{c}} 1&1&1\\ 1&{1 + {\rm{x}}}&1\\ 1&1&{1 + {\rm{y}}} \end{array}} \right|\)

Applying R₂ → R₂ – R₁, R₃ → R₃ – R₁, we get

\(= \left| {\begin{array}{*{20}{c}} 1&1&1\\ 0&{\rm{x}}&0\\ 0&0&{\rm{y}} \end{array}} \right|\)

Now, Expanding along C₁

= 1 (xy – 0) – 0 + 0 = xy