Linear Equations

The given system of linear equations is: We can write this system in matrix form as: Let the matrix be , the column matrix of variables be , and the constant matrix be : To solve for , we find . The inverse of matrix is given by: where . So, Now, multiply with : Performing the matrix multiplication: Thus, the point common to the paths of the ants is .

Let the number of books sold for each subject on day I and day II be represented by matrices. The total sale can be calculated by multiplying the price of each book by the number of books sold.
The number of books sold on day I is given by: The number of books sold on day II is given by: The price of each book is given by: The total sale matrix is the sum of the sales on day I and day II: Performing the matrix multiplication: Thus, the total sale in two days is .
The cost price of all the books is . Hence, the profit is: Thus, the profit earned after the sale of two days is .