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The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

$\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 = $Rs.20160$
answered Feb 14, 2013 by sreemathi.v
edited Mar 1, 2013 by balaji.thirumalai

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