A= ( −2 −1 2 −2 2 3 −4 1 3 ) b = ( −1 −1 4 ) x = ( x1 x2 x3 ) (a) (2 pts) write down the augmented matrix (a|b). (b) (4 pts) use gauss-jordan elimination to find the reduced row echelon form (rref) of the augmented matrix. (c) (2 pts) what is the rank of a? what is the rank of (a|b) (d) (2 pts) state whether the system is consistent or inconsistent. state how many solutions the system has; if there is/are a solution/s, write it/them down.

The augmented matrix is

The Reduced Row Echelon Form of the augmented matrix is

The rank of matrix (A|B) is 3

The system is consistent and the solutions are

Step-by-step explanation:

We have the following information:

    1. The augmented matrix is

We take the matrix A and we add the matrix B we use a vertical line to separate the coefficient entries from the constants.

    2. To transform the augmented matrix to the Reduced Row Echelon Form (RREF) you need to follow these steps:

    3. What is the rank of (A|B)

To find the rank of a matrix, we simply transform the matrix to its row echelon form and count the number of non-zero rows.

Because the row echelon form of the augmented matrix has three non-zero rows the rank of matrix (A|B) is 3

   4. Solutions of the system

This definition is very important: "A system of linear equations is called inconsistent if it has no solutions. A system which has a solution is called consistent"

This system is consistent because from the row echelon form of the augmented matrix we find that the solutions are (the last column of a row echelon form matrix always give you the solution of the system)

by definition, an arc subtended by a central angle of some given measure has the same measure. so .