Question

Without expanding determinants, find the value of `|(2014, 2017, 1),(2020, 2023, 1),(2023, 2026, 1)|`

Answer 1

Let D = `|(2014, 2017, 1),(2020, 2023, 1),(2023, 2026, 1)|`

Applying C₂ → C₂ – C₁, we get

D = `|(2014, 3, 1),(2020, 3, 1),(2023, 3, 1)|`

Taking (3) common from C₂, we get

D = `3|(2014, 1, 1),(2020, 1, 1),(2023, 1, 1)|`

= 3(0)           ...[∵ C₂ and C₃ are identical]
= 0