Question

If A = `[(0, 1, c), (-1, a, -b), (2, 3, 0)]` is a skew-symmetric matrix, then the value of a + b + c = ______.

Options

• 1

• 2

• 3

• 4

Answer 1

If A = `[(0, 1, c), (-1, a, -b), (2, 3, 0)]` is a skew-symmetric matrix, then the value of a + b + c = 1.

Explanation:

A = `[(0, 1, c), (-1, a, -b), (2, 3, 0)]`

When the matrix A is skew symmetric then A^T = −A ⇒ a_ij = a_ji;

⇒ c = −2; a = 0 and b = 3

So, a + b + c = 0 + 3 − 2 = 1.