Mathematics

Problem

Consider the matrices

M=\begin{bmatrix}p+q & 3r & 1\\ 2p & q-p & s\end{bmatrix},\quad N=\begin{bmatrix}8 & 9 & 1\\ 10 & -2 & s\end{bmatrix}.

It is given that

M=N

. a. (i) By comparing

M

and

N

, write the equations relating

p,\,q,\,r

and

s

. b. (ii) Solve these equations to find

p,\,q

and

r

. c. (iii) What can you conclude about the parameter

s

? Justify your answer.