To calculate: The solution set of the system of equations,
With help of the inverse of coefficient matrix.
Answer to Problem 39E
The solution set of the system of equations is
Explanation of Solution
Given information:
The system of equations is provided below,
Formula used:
The solution set of the system of equations with same number of equations and variables is given by,
For a matrix A , the inverse of a
Calculation:
Consider the system of equations as,
Now, in the above system of equation we have two equations and two variables x and y.
Construct a coefficient matrix P ,
Secondly, the variable matrix X is given as,
Thirdly, matrix of constants Q which is given on right hand of the equation is,
Therefore, write the system as,
First, find the inverse of the matrix,
Let the inverse of the matrix be
Use the relation,
Now, multiply the above two matrices, to get,
Now, equate the corresponding elements of the two matrices. First write the system of equations when equated to the first column,
Now, write the system of equations when equated to the second column,
So, get the two augmented matrices which are as follows:
Combing the above two matrices such that the identity matrix is on the right hand side, to get,
Now, apply the Gauss-Jordan elimination to find the inverse of
First to make the entry
Next, to make the entry
Next, to make the entry
Next, to make the entry
Therefore, the inverse of the matrix
Now, substituting the values of
Therefore, the value of x is 5 and y is
Thus, the solution set of the system of equations is
Chapter 8 Solutions
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