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.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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.

Approved by eNotes Editorial Team