Question

If A = `[(a, c, -1),(b, 0, 5),(1, -5, 0)]` is a skew-symmetric matrix, then the value of 2a − (b + c) is _______.

Options

• 0

• 1

• −10

• 10

Answer 1

If A = `[(a, c, -1),(b, 0, 5),(1, -5, 0)]` is a skew-symmetric matrix, then the value of 2a − (b + c) is 0.

Explanation:

We know that, if matrix A is skew symmetric, then 

A' = −A

∴ `[(a, b, 1),(c, 0, -5),(-1, 5, 0)] = [(-a, -c, 1),(-b, 0, -5),(-1, 5, 0)]`

On comparing matrices, we get

a = −a ⇒ 2a = 0 ⇒ a = 0

b = −c and c = −b

Now, 2a + (b + c)

= 2 × 0 + (b − b)

= 0