Question

`[(3c + 6, a - d),(a + d, 2 - 3b)] = [(12, 2),(-8, -4)]` are equal, then value of ab – cd is ______.

Options

• 4

• 16

• –4

• –16

Answer 1

`[(3c + 6, a - d),(a + d, 2 - 3b)] = [(12, 2),(-8, -4)]` are equal, then value of ab – cd is 4.

Explanation:

Given, `[(3c + 6, a - d),(a + d, 2 - 3b)] = [(12, 2),(-8, -4)]`

∴ 3c + 6 = 12  ...(i)

a – d = 2  ...(ii)

a + d = –8  ...(iii)

2 – 3b = –4  ...(iv)

From equation (i), we get c = 2

On solving equations (ii) and (iii), we get a = –3 and d = –5

From equation (iv), we get b = 2

Now, ab – cd = (–3)2 – 2(–5)

`\implies` ab – cd = –6 + 10 = 4