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

rakesh05's profile pic

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

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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.

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pramodpandey | College Teacher | (Level 3) Valedictorian

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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.