List of top Applied Mathematics Questions on System of Linear Equations

Tabulate the trend values of the years and compute the expected sales trend for the year 2002.
If \( R_2 \) is the feasible region, then what are the other two non-trivial constraints?
If \( R_1 \) is the feasible region, then what are the other two non-trivial constraints?
Find the inverse of matrix \( A \).
Write the system of linear equations in \( x \) and \( y \) formed from the given situation.
Determine the probability that the student studied for at least 2 hours.
A cistern has three pipes A, B, and C. Pipes A and B are inlet pipes, whereas C is an outlet pipe. Pipes A and B can fill the cistern separately in 3 hours and 4 hours respectively, while pipe C can empty the completely filled cistern in 1 hour. If the pipes A, B, and C are opened in order at 5, 6, and 7 a.m. respectively, at what time will the cistern be empty?
Give a linear equation that describes the computer system's book value at the end of \( t \)th year, where \( 0 \leq t \leq 3 \).
The mean weekly sales of a 4-wheeler was 50 units per agency in 20 agencies. After an advertising campaign, the mean weekly sales increased to 55 units per agency with a standard deviation of 10 units. Test whether the advertising campaign was successful.
[Given \( \sqrt{5} = 2.24 \), \( t_{19}(0.05) = 1.729 \)]
Evaluate \( \int_{0}^{1} \frac{e^{-x}}{1 + e^x} \, dx \).

A man bought an item for ₹ 12,000. At the end of the year, he decided to sell it for ₹ 15,000. If the inflation rate was 6%, find the nominal and real rate of return.

Given matrix equation: \[ \begin{bmatrix} x - y & 2x + z \\ 2x - y & 3z + w \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix} \] Find the values of \( x, y, z, \) and \( w \).
In an LPP, if the objective function \( Z = ax + by \) has the same maximum value on two corner points of the feasible region, then the number of points at which the maximum value of \( Z \) occurs is: