# 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.

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### 2 Answers

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.

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.**