The augmented matrix of a system of equations has been trans

The augmented matrix of a system of equations has been transformed to an equivalent matrix in row-echelon form. Using x, y, and z as variables, write the system of equations corresponding to the following matrix. If the system is consistent, solve it. 12 1 0 1 -3 9 0 0 1 2 Which of the following system of equations corresponds to the given matrix? OB. 2x + y + 5z = 1 -3y +9z = 1 y-3z = 9 z--2 O D. Oc. 2x + y = 5 -3y = 9 2x ty 9 1x-3y+z -2 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. 0 A. There is one solution. The solution set is { Simplify your answer. Type an ordered triple, using integers or fractions.) z)) where z is any real number Type expressions using z as the variable. Simplify your answers) ° C. The system is inconsistent. Click to select and enter your answer(s)

Solution

from the row echelon form

the equation that corresponds to given matrix is

x + 2y + z = 5

y - 3z = 9

z = -2

so, option a is correct

b) solving the system by back substitution

z =-2

y = 9 + 3(-2) = 3

x = 5 - 2y - z

x = 5 - 2(3) -(-2)

x = 1

hence, solution is

{ 1 , 3 , -2 }