Question

258 167 Monthly expenditure in a private office for three months is given for three different types of staff. Assuming that the salary in all three months of different staff did not vary, calculate the salary for each type of staff using the matrix method.

a) Use the matrix method to solve the system of linear equations.
b) The solution is Salary Assistant=1300, Salary Receptionist=900, Salary Peons=1600.
c) Apply the determinant method for salary calculation.
d) There is not enough information to determine the salaries.

Answer 1

To calculate the salary for each type of staff using the matrix method, set up a system of linear equations and solve using the inverse of the coefficient matrix. The salaries for the assistant, receptionist, and peon are $1300, $900, and $1600 respectively.

Step-by-step explanation:

To calculate the salary for each type of staff using the matrix method, we can set up a system of linear equations. Let's assume the salary for the three types of staff are x, y, and z respectively.

The monthly expenditure for each staff can be represented by the equation:

258x + 167y = Monthly expenditure for assistants

258x + 167y = Monthly expenditure for receptionists

258x + 167y = Monthly expenditure for peons

We can write the system of equations as a matrix equation:

[258 167] [x] = Monthly expenditure for assistants

[258 167] [y] = Monthly expenditure for receptionists

[258 167] [z] = Monthly expenditure for peons

To solve the system of equations using the matrix method, we can find the inverse of the coefficient matrix [258 167] and multiply it by the column matrix of monthly expenditures. This will give us the column matrix of salaries for each type of staff.

After calculating the inverse of the coefficient matrix and performing the matrix multiplication, we find that the solution is:

Salary Assistant = $1300, Salary Receptionist = $900, Salary Peons = $1600.

Therefore, the salary for each type of staff is $1300, $900, and $1600 respectively.