Apply the Gaussian elimination method on the following augmented matrix. Determine the rank and nullity of the coefficient matrix. Determine the basic and free variables and find the solution. 2 1 -8 1 -2 -3 1 -1 1 2 3

se row operations on the augmented matrix as far as necessary to determine whether the system is independent, dependent, or inconsistent. 5x 3y+ 3z=13 10x 6y+ 6z=24 -10x+ 6y- 6z = -24 Is the system is independent, dependent, or inconsistent? OA. independent OB. inconsistent OC. dependent

Determine whether the statement below is true or false. Justify the answer. The equation Ax=b is consistent if the augmented matrix [a b] has a pivot position in every row. Choose the correct answer below. C A. This statement is false. The augmented matrix A b than rows. OB. This statement is true. The pivot positions in the augmented matrix [ A b] always occur in the columns that represent A. OC. This statement is true. If the augmented matrix [ A b] has a pivot position in every row, then the equation Ax=b has a solution for each b in R™. cannot have a pivot position in every row because it has more columns D. This statement is false. If the augmented matrix [ A b] has a pivot position in every row, the equation Ax = b may or may not be consistent. One pivot position may be in the column representing b.

Find the inverse matrix for the matrix of coefficients of thie system below. Then, use It to find the solution to system. 3 solutionl solution2 solution3 Inversc: solution4 solution5 solutiono solution7 solution8 solutiong |L ||||