Question

If `[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)]` is skew – symmetric find the values of p, q and r

Answer 1

Let A = `[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)]`

A^T = `[(0, 2, "r"),("p", "q"^2, 1),(3, -1, 0)]`

A is skew-symmetric if A = – A^T 

`[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)] = - [(0, 2, "r"),("p", "q"^2, 1),(3, -1, 0)]`

`[(0, "p", 3),(2, "q"^2, -1),("r", 1, 0)] = [(0, -2, -"r"),(-"p", -"q"^2, -1),(-3, 1, 0)]`

Equating the corresponding entries.

p = – 2, r = – 3

q² = – q² 

⇒ q² + q² = 0

⇒ 2q² = 0

⇒ q = 0

∴ The required values are

p = – 2, q = 0, r = – 3