Question

If the matrix A = `[(0, r, -2),(3, p, t),(q, -4, 0)]` is skew-symmetric, then the value of `(q + t)/(p + r)` is ______.

Options

• –2

• 0

• 1

• 2

Answer 1

If the matrix A = `[(0, r, -2),(3, p, t),(q, -4, 0)]` is skew-symmetric, then the value of `(q + t)/(p + r)` is –2.

Explanation:

In a skew symmetric matrix A' = −A

Putting values:

`[(0, r, -2),(3, p, t),(q, -4, 0)] = -[(0, 3, q),(r, p, -4),(-2, t, 0)]`

`[(0, r, -2),(3, p, t),(q, -4, 0)] = [(-0, -3, -q),(-r, -p, -(-4)),(-(-2), -t, -0)]`

`[(0, r, -2),(3, p, t),(q, -4, 0)] = [(0, -3, -q),(-r, -p, 4),(2, -t, -0)]`

Since matrices are equal, their corresponding terms are equal.

So, r = −3, t = 4, q = 2

And p = −p

p + p = 0

2p = 0

p = 0

Now, we need to find

`(q + t)/(p + r) = (2 + 4)/(0 + (-3))`

= `6/(-3)`

= `(-6)/3`

= −2