$\begin{array}{1 1} 20061 \\ 21600 \\ 20160 \\ 20016 \end{array} $

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- With these type of word problems, we need to set up the correct matrix multiplication and solve for the unknown variables.
- Multiplication of two matrices is defined only if the number of columns of the left matrix is the same as the number of rows of the right matrix.
- If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B: $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$

The number of Chemistry books in the school is 10 dozen = 10 x 12 = 120.

The number of Physics books in the school is 8 dozen = 8 x 12 = 96.

The number of Chemistry books in the school is 10 dozen = 10 x 12 = 120.

The number of books can be represented by matrix $A$ of order $1\times 3$ as follows: $A=\begin{bmatrix} 120& 96& 120\end{bmatrix}$

The cost of each book of chemistry,physics and economics are $Rs.80$,$Rs.60$,$Rs.40$ respectively.

The cost of the books can be represent by the matrix $B$ of order $3\times 1$ as follows: $\begin{bmatrix}80\\60\\40\end{bmatrix}$

The total amount received by selling all the books can be represented by matrix multiplication as follows: $AB=\begin{bmatrix} 120& 96& 120\end{bmatrix} \begin{bmatrix}80\\60\\40\end{bmatrix}$

$\Rightarrow AB = [120\times 80+96\times 60+120\times 40]$

$\Rightarrow AB = [9600+5760+4800]$

$\Rightarrow AB = [20160]$

Therefore, the total amount received = $Rs.20160$

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