Given, 

The details of stock of various types of books.

Physics : 10 dozen books 

Chemistry : 8 dozen books 

Mathematics : 5 dozen books

Hence, the number of dozens of books available in the store can be represented in matrix form with each column corresponding to a different subject as -

X = [10 8 5]

The price of each of the items is also given. 

Cost of one physics book = Rs 8.30 

⇒ Cost of one dozen physics books = 12 × Rs 8.30

∴ Cost of one dozen physics books = Rs 99.60 

Cost of one chemistry book = Rs 3.45 

⇒ Cost of one dozen chemistry books = 12 × Rs 3.45 

∴ Cost of one dozen chemistry books = Rs 41.40 Cost of one mathematics book = Rs 4.50 

⇒ Cost of one dozen mathematics books = 12 × Rs 4.50 

∴ Cost of one dozen mathematics books = Rs 54

Hence, the cost of purchasing a dozen books of each subject can be represented in matrix form with each row corresponding to a different subject as –

Y =\(\begin{bmatrix} 99.60 \\[0.3em] 41.60 \\[0.3em] 54 \end{bmatrix}\)

Now, 

The amount received by the store upon selling all the available books can be found by taking the product of the matrices X and Y.

XY = [10 8 5] \(\begin{bmatrix} 99.60 \\[0.3em] 41.60 \\[0.3em] 54 \end{bmatrix}\)

⇒ XY = [10 × 99.60 + 8 × 41.40 + 5 × 54]

⇒ XY = [996 + 331.20 + 270]

∴ XY = [1597.20]

Thus, 

The total amount the store will receive from selling all the items is Rs 1597.20.