Question

Find a, b, c and d if `3[(a, b),(c, d)] = [(4, a + b),(c + d, 3)] + [(a, 6),(-1, 2d)]`

Answer 1

Given
`3[(a, b),(c, d)] = [(4, a + b),(c + d, 3)] + [(a, 6),(-1, 2d)]`

⇒ `[(3a, 3b),(3c, 3d)] = [(4 + a, a + b + 6),(c + d - 1,3 + 2d)]`
Comparing the corresponding elements:
3a = 4 + a
⇒ 3a – a = 4
⇒ 2a = 4
∴ a = 2
3b = a + b + 6
⇒ 3b – b = 2 + 6
⇒ 2b = 8
∴ b = 4
3d = 3 + 2d
⇒ 3d - 2d = 3
∴ d = 3
3c = c + d – 1
⇒ 3c – c = 3 – 1
2c = 2
⇒ c = 1
Hence a = 2, b = 4, c = 1, d = 3.