Question

Find the values of p, q, r, and s if

`[("p"^2 - 1, 0, - 31 - "q"^3),(7, "r" + 1, 9),(- 2, 8, "s" - 1)] = [(1, 0, -4),(7, 3/2, 9),(-2, 8, -pi)]`

Answer 1

`[("p"^2 - 1, 0, - 31 - "q"^3),(7, "r" + 1, 9),(- 2, 8, "s" - 1)] = [(1, 0, -4),(7, 3/2, 9),(-2, 8, -pi)]`

Equating the corresponding entries

⇒ p² – 1 = 1

⇒ p² = 1 + 1 = 2

p = `+-  sqrt(2)`

– 31 – q³ = -4

– q³ = – 4 + 31 = 27

q³ = – 27 = (– 3)³

⇒ q = – 3

r + 1 = `3/2`

⇒ r = `3/2 - 1 = (3 - 2)/2 = 1/2`

s – 1 = π

⇒ s = – π + 1

(i.e.,) s = 1 – π

So, p = `+-  sqrt(2)`

q = – 3

r = `1/2` and s = 1 – π