What can you say about the solutions of this system? The augmented matrix of a linear system with three variables and four equations has rank of 4.

2 Answers | Add Yours

rakesh05's profile pic

rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted on

The augmented matrix is [A:b].

Given rank ([A:b])=4

Because the number of variables in the system is three so the rank of the coefficient matrix A is 3.

The condition for the system to be consistent(Have a solution) is that  rank([A:b])=rank(A).

Here we see that rank([A:b]) is not equal to rank (A). So the given system is inconsistent i.e. no solution.

pramodpandey's profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

The augmented matrix is [A:b].

Given rank of [A:b] =4

The rank of [A] will be less or equal to 3

So  rank [A:b] , can not equal to rank (A). So the given system has   no solution.

If no. of equations more than no. of variables in equation ,such system has no solution.

We’ve answered 318,957 questions. We can answer yours, too.

Ask a question