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

Answer 1

Answer: hello your question is disorganized attached below is the question and solution

answer:

1) The system has a unique solution ( x = 0, y = 0 ) ( D )

2) The system has a unique solution ( x = 0, y = 3, z = 3 ) ( D )

Explanation:

1 )
`\left[\begin{array}{ccc}1&0\\0&1\\0&0\end{array}\right] \left[\begin{array}{ccc}0\\0\\0\end{array}\right]` this matrix is a homogenous since there are three(3) equations and 2 variables

hence the system has a unique solution ( attached below )

2) Attached below

The matrix is a Non-homogenous system since it comprises of three(3) equations and 2 variables