Solve the system of linear equations using elementary row operations on an augmented matrix. This problem will have you enter intermediate steps of the solution.

⎧⎪⎨⎪⎩4x+5y−2z=−1y+2z=−2x+y−z=1{4x+5y-2z=-1y+2z=-2x+y-z=1

(a) Fill in the corresponding augmented matrix. The rightmost column represents the constant values from the linear equations.    

(b) Use elementary row operations on the augmented matrix in part (a) to make a matrix of the form

⎡⎢⎣1abc01de001f⎤⎥⎦[1abc01de001f], ⎡⎢⎣1abc01de0001⎤⎥⎦[1abc01de0001], ⎡⎢⎣1abc001d0000⎤⎥⎦[1abc001d0000], or ⎡⎢⎣1abc000d0000⎤⎥⎦[1abc000d0000].*

     

(c) Use elementary row operations on the augmented matrix in part (b) to make a matrix of the form

⎡⎢⎣100a010b001c⎤⎥⎦[100a010b001c], ⎡⎢⎣10a001c00001⎤⎥⎦[10a001c00001], or ⎡⎢⎣1a0b001c0000⎤⎥⎦[1a0b001c0000], or ⎡⎢⎣1ab000010000⎤⎥⎦[1ab000010000].      

(d) Using the matrix from in part (c), determine the solution of the corresponding system of linear equations. If the system has no solution or is inconsistent, enter DNE for all answers. If there are infinite number of solutions, enter zz for zz and find xx and yy in terms of zz. Enter only integer numbers or reduced fractions.

x=x=   

y=y=   

z=z=