Question

Convert the system + = -5 X1 -2x1 2x1 4x2 8x2 8x2 + X3 = 13 -7 + + X3 to an augmented matrix. Then reduce the system to echelon form and determine if the system is consistent. If the system in consistent, then find all solutions. Augmented matrix: [[1,4,0,-5], [-2,-8,1,13], [2,8,1,-7]] Echelon form: Is the system consistent? yes Solution: (x1, X2, X3) = + S1, + Si, + S1

Answer 1

To convert the system to an augmented matrix, perform row operations. Then, reduce the system to echelon form and determine if it is consistent. If so, find all solutions.

Step-by-step explanation:

1. Convert the system + = -5 X1 -2x1 2x1 4x2 8x2 8x2 + X3 = 13 -7 + + X3 to an augmented matrix.
   The augmented matrix is: [[1,4,0,-5], [-2,-8,1,13], [2,8,1,-7]].
2. Reduce the system to echelon form.
   The echelon form is: [[1,4,0,-5], [0,0,1,4], [0,0,0,0]].
3. Determine if the system is consistent.
   Since there is a row of zeroes in the echelon form, the system is consistent.
4. Find all solutions if the system is consistent.
   Since the system is consistent, there are infinitely many solutions.
   The solutions can be represented as (x1, x2, x3) = (s1, s2, s3), where s1, s2, and s3 are arbitrary constants.