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Solve the following system using augmented matrix methods: 2x1 - 5x2 + 5x3 = -33 2x1 + 0x2 + 3x3 = -16 7x1 + 0x2 + 9x3 = -47 (a) The initial matrix is: [2 -5 5 | -33] [2 0 3 | -16] [7 0 9 | -47] (b) First, perform the Row Operation 12R1 â†’ R1. The resulting matrix is: [24 -60 60 | -396] [2 0 3 | -16] [7 0 9 | -47] (c) Next, perform the operations -2R1 + R2 â†’ R2 -7R1 + R3 â†’ R3. The resulting matrix is: [24 -60 60 | -396] [0 120 -117 | 764] [0 420 -423 | 2719] (d) Finish simplifying the augmented matrix down to reduced row echelon form. The reduced matrix is: [1 0 0 | -3] [0 1 0 | 5] [0 0 1 | -7] Remember: This matrix must be simplified all the way to reduced form. (e) How many solutions does the system have? If infinitely many, enter "Infinity". The system has a unique solution. (f) What are the solutions to the system? x1 = -3 x2 = 5 x3 = -7 Note: If there are no solutions, write "No Solution" or "None" for each answer. If there are infinitely many solutions, and the solution set describes a line (that is, if there is only one free variable), set x3 = t and solve for the remaining variables in terms of t. If there are infinitely many solutions, and the solution set describes a plane (that is, if the solution set has two free variables), set the variables x3 = t and x2 = s, and then solve for x1 in terms of s and t.

          Solve the following system using augmented matrix methods:
2x1 - 5x2 + 5x3 = -33
2x1 + 0x2 + 3x3 = -16
7x1 + 0x2 + 9x3 = -47

(a) The initial matrix is:

[2 -5 5 | -33]
[2 0 3 | -16]
[7 0 9 | -47]

(b) First, perform the Row Operation 12R1 â†’ R1. The resulting matrix is:

[24 -60 60 | -396]
[2 0 3 | -16]
[7 0 9 | -47]

(c) Next, perform the operations
-2R1 + R2 â†’ R2
-7R1 + R3 â†’ R3.
The resulting matrix is:

[24 -60 60 | -396]
[0 120 -117 | 764]
[0 420 -423 | 2719]

(d) Finish simplifying the augmented matrix down to reduced row echelon form. The reduced matrix is:

[1 0 0 | -3]
[0 1 0 | 5]
[0 0 1 | -7]

Remember: This matrix must be simplified all the way to reduced form.

(e) How many solutions does the system have? If infinitely many, enter "Infinity".

The system has a unique solution.

(f) What are the solutions to the system?
x1 = -3
x2 = 5
x3 = -7

Note: If there are no solutions, write "No Solution" or "None" for each answer. If there are infinitely many solutions, and the solution set describes a line (that is, if there is only one free variable), set x3 = t and solve for the remaining variables in terms of t. If there are infinitely many solutions, and the solution set describes a plane (that is, if the solution set has two free variables), set the variables x3 = t and x2 = s, and then solve for x1 in terms of s and t.

Added by Thomas F.

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