Question

Solve: `|(x,2,-1),(2,5,x),(-1,2,x)|` = 0

Answer 1

Expanding along R₁ we get

`x|(5,x),(2,x)| - 2|(2,x),(-1,x)| - 1|(2,5),(-1,2)|` = 0

⇒ x(5x - 2x) - 2(2x + x) - 1(4 + 5) = 0

⇒ x(3x) - 2(3x) - 1(9) = 0

⇒ 3x² - 6x - 9 = 0

⇒ x² - 2x - 3 = 0   ....(Divided by 3)

⇒ (x - 3)(x + 1) = 0

⇒ x = 3 or -1