Describe the procedure for finding the general solution of a system of three linear equations involving p, q, and r if its reduced matrix indicate has one row of zeros at the bottom. You may assume that the coefficients in the augmented matrix correspond to variables in alphabetical order from left to right.
A)Use the reduced matrix to find equations for each variable p, q, and r. These equations can be used as the general solution to the system of equations.
B)Use the reduced matrix to find a general equation for p in terms of q and r. This equation can be used as the general solution to the system of equations.
C)Use the reduced matrix to solve for p and q in terms of r. These solutions will be valid for any real value of r.
D)Use the reduced matrix to solve for r in terms of p and q. This solution will be valid for any real value of p and q.
E)It is not possible to find a general solution for a system of three linear equations if its reduced matrix indicates an infinite number of solutions.

Question

Describe the procedure for finding the general solution of a system of three linear equations involving p, q, and r if its reduced matrix indicate has one row of zeros at the bottom. You may assume that the coefficients in the augmented matrix correspond to variables in alphabetical order from left to right. ​
A)Use the reduced matrix to find equations for each variable p, q, and r. These equations can be used as the general solution to the system of equations.
B)Use the reduced matrix to find a general equation for p in terms of q and r. This equation can be used as the general solution to the system of equations.
C)Use the reduced matrix to solve for p and q in terms of r. These solutions will be valid for any real value of r.
D)Use the reduced matrix to solve for r in terms of p and q. This solution will be valid for any real value of p and q.
E)It is not possible to find a general solution for a system of three linear equations if its reduced matrix indicates an infinite number of solutions.

Quizplus · Accepted Answer

If the reduced matrix has one row of zeroes at the bottom, it means that there is one free variable in the system (in this case, r). Therefore, we can solve for p and q in terms of r, which gives us a general solution that is valid for any value of r. Solving for r in terms of p and q is not possible with this information, as there is still a free variable in the system. Option A is also not the best choice, as it would involve solving for each variable separately and would not give us a solution in terms of one free variable. Option B would only give us a solution in terms of two variables, but we need a general solution in terms of all three variables. Option E does not apply, as the reduced matrix indicates a unique solution (one row of zeroes indicates one free variable, which gives us a unique solution).

Describe the Procedure for Finding the General Solution of a System