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Find the values of p, q, r and s if \(\begin{bmatrix} p^2 -1 & \ 0 &-31 - q^3 \\[0.3em] 7 &r + 1& 9\\[0.3em] -2 &8 & s - 1 \end{bmatrix}\)\(\begin{bmatrix} 1& \ 0 &-4 \\[0.3em] 7 &3/2& 9\\[0.3em] -2 &8 & π \end{bmatrix}\)

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When two matrices (of same order) are equal then their corresponding entries are equal.

Here \(\begin{bmatrix} p^2 -1 & \ 0 &-31 - q^3 \\[0.3em] 7 &r + 1& 9\\[0.3em] -2 &8 & s - 1 \end{bmatrix}\)\(\begin{bmatrix} 1& \ 0 &-4 \\[0.3em] 7 &3/2& 9\\[0.3em] -2 &8 & π \end{bmatrix}\)

⇒ p2 – 1 = 1 

⇒ p2 = 1 + 1 = 2 

p = ± √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 = ± √2, q = -3, r = 1/2 and s = 1 – π

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