Question

Find the values of x, y and z if `[(x + 2, 6),(3, 5z)] = [(-5, y^2 + y),(3, 20)]`

Answer 1

Comparing the corresponding elements of equal determinents,
x + 2 = -5
⇒ x = –5 – 2 = –7
∴ x = –7, 5z = –20
⇒ z = `-(20)/(5)`
= –4
⇒ y²  + y = 6
⇒ y² + y – 6 = 0
⇒ y² + 3y – 2y – 6 = 0
⇒ y(y + 3) – 2(y + 3) = 0
⇒ (y + 3)(y – 2) = 0
Either y + 3 = 0,
then y = –3 or y – 2 = 0,
then y = 2
Hence x = –7, y = –3, 2, z = –4.