Question

Use the matrix inverse and the matrix division method to solve the following set for x and y in terms of c:

Answer 1

MuPAD can be used to solve both symbolic and numeric types of calculations. MuPAD can be run by entering mupadwelcome in the command window.

 

To find the solution of a set of linear equations, the matrix inverse method can be used in which the inverse of a matrix can be calculated using the inverse function.

 

Also, the division method can be used to obtain the solution.

 

To calculate the product of a matrix and compare it with a new matrix with its variable substituted, enter the following lines in MuPAD:

 

Define the matrices:

A:=matrix([[4*c, 5], [3, -4]]);B:=matrix([[43], [-22]]);

The result obtained is:

Define the matrices:

 

Solution using Matrix inverse method can be done as:

 

Solution using division method can be done as:

 

To obtain the solution using matrix inverse method, enter the following code in the MuPAD window as:

Solution using Matrix inverse method can be done as:

inverse(A)*B;

simplify(%)

Define the matrices:

 

Solution using Matrix inverse method can be done as:

 

Solution using division method can be done as:

 

The result obtained is:

To obtain the solution using matrix division method, enter the following code in the MuPAD window as:

 

Solution using division method can be done as:

1/A*B;

simplify(%)

 

The result obtained is:

 

Define the matrices:

 

Solution using Matrix inverse method can be done as:

 

Solution using division method can be done as:

 

Thus, the solution of a given set of equations can be calculated using both the matrix inverse method and the division method.

Thus, the solution of a given set of equations can be calculated using both the matrix inverse method and the division method.