Question

The reduced row echelon form of a system of linear equations in x and y or in x, y and z is given. For each system, determine whether it has a unique solution (in this case, find the solution), infinitely many solutions, or no solutions.

1. [ 1 0 I 0 ]

    [ 0 1 I 0 ]

    [ 0 0 I 0 ]

A. No solutions
B. Infinitely many solutions
C. Unique solution: x=1,y=1,z=0
D. Unique solution: x=0,y=0
E. Unique solution: x=0,y=0,z=0
F. None of the above

2. [ 1 0 0 I -1 ]

    [ 0 1 0 I 3 ]

    [ 0 0 0 I 2 ]

A. Infinitely many solutions
B. Unique solution: x=−1,y=3,z=0
C. Unique solution: x=−1,y=3,z=2
D. No solutions
E. Unique solution: x=−1,y=3
F. None of the above

3. [ 1 0 0 I -4 ]

     [ 0 1 0 I 3 ]

     [ 0 0 0 I 0 ]

A. Unique solution: x=0,y=0,z=0
B. Unique solution:x=−4,y=3
C. Infinitely many solutions
D. Unique solution: x=3,y=−4
E. No solutions
F. None of the above

4. [ 1 0 0 I 0 ]

     [ 0 1 0 I 4 ]

     [ 0 0 1 I 4 ]

A. Unique solution: x=4,y=4
B. Unique solution: x=0,y=4
C. Unique solution: x=0,y=4,z=4
D. Infinitely many solutions
E. No solutions
F. None of the above

Answer 1