Question

If A = `[(p/4, 0, 0), (0, q/5, 0), (0, 0, r/6)]` and `"A"^-1 = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`, then p + q + r = ______ 

विकल्प

• 25

• 39

• 68

• 77

Answer 1

If A = `[(p/4, 0, 0), (0, q/5, 0), (0, 0, r/6)]` and `"A"^-1 = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`, then p + q + r = 77

Explanation:

If B = `[(a, 0, 0), (0, b, 0), (0, 0, c)]`, then `"B"^-1[(1/a, 0, 0), (0, 1/b, 0), (0, 0, 1/c)]`

∴ `"A"^-1 = [(4/p, 0, 0), (0, 5/q, 0), (0, 0, 6/r)] = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`

⇒ `4/p = 1/4` ⇒ p = 16,

`5/q = 1/5 ⇒ q = 25` and

`6/r = 1/6 ⇒ r = 36`

∴ p + q + r = 16 + 25 + 36 = 77