Find p,q,r and s if [(p+4)(2q-7),(s-3) (r+2s)] = [(6 -3),(2 14)]

Question

Find p,q,r and s if \(\begin{bmatrix} p+4 & 2q-7\\[0.3em] s-3 &r+2s\end{bmatrix} \) = \(\begin{bmatrix} 6 & -3 \\[0.3em] 2 & 14\end{bmatrix}\)

Answer 1

Two matrices are equal, if the corresponding elements are equal, i.e., p + 4 = 6 ⇒ p = 6 – 4 = 2 

2q – 7 = –3 ⇒ 2q = –3 + 7 = 4 ⇒ q = 2 

s - 3 = 2 ⇒ s = 5

r + 2s = 14 ⇒ r + 10 = 5 ⇒ r = -5