Question

Evaluate: `|(x^2 - x + 1, x - 1),(x + 1, x + 1)|`

Answer 1

We have, `|(x^2 - x + 1, x - 1),(x + 1, x + 1)|`

[Applying C₁ → C₁ – C₂]

= `|(x^2 - 2x + 2, x - 1),(0, x + 1)|`

= (x² – 2x + 2) · (x + 1) – (x – 1) · 0

= x³ – 2x² + 2x + x² – 2x + 2

= x³ – x² + 2