Please reply fast..Three shopkeepers A, B and C go to a store to buy stationary. A purchases 12 dozen notebooks, 5 dozen pens and 6 dozen pencils. B purchases 10 dozen notebooks, 6 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks, 13 dozen pens and 8 dozen pencils. A notebook cost 40 paise, a pen costs rs 1.25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual's bills.

$\begin{array}{ccc}N.B& Pen& Pencil\end{array}\phantom{\rule{0ex}{0ex}}P=\begin{array}{c}A\\ B\\ C\end{array}{\left[\begin{array}{ccc}12& 5& 6\\ 10& 6& 7\\ 11& 13& 8\end{array}\right]}_{3\times 3}$

Now,

Cost on 1 notebook = 40 paise

Cost if 1 dozen (12) notebooks = Rs(0.40*12)

= Rs 4.8

Cost on 1 pen = Rs 1.25

Cost if 1 dozen (12) pen = Rs (1.25*12)

= Rs 15

Cost on 1 pencil = 35 paise

Cost if 1 dozen (12) pencil = Rs ( 0.35*12 )

= Rs 4.2

Next, let the cost matrix be Q. So

$Q={\left[\begin{array}{c}4.8\\ 15\\ 4.2\end{array}\right]}_{3\times 1}$

Now, multiply matrix P and Q to calculate the bill of each shopkeeper. So,

$PQ=\left[\begin{array}{ccc}12& 5& 6\\ 10& 6& 7\\ 11& 13& 8\end{array}\right]\left[\begin{array}{c}4.8\\ 15\\ 4.2\end{array}\right]\phantom{\rule{0ex}{0ex}}=\left[\begin{array}{c}57.60+75+25.20\\ 48+90+29.40\\ 52.80+195+33.60\end{array}\right]\phantom{\rule{0ex}{0ex}}=\left[\begin{array}{c}157.80\\ 167.40\\ 281.40\end{array}\right]$

Therefore,

**Bill of shopkeeper A = Rs 157.80**

Bill of shopkeeper B = Rs 167.40

Bill of shopkeeper C = Rs 281.40

Bill of shopkeeper B = Rs 167.40

Bill of shopkeeper C = Rs 281.40

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