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What is the solution of the system of equations represented by the row-echelon form of the augmented matrix?

a) x = 9/4, y = 3/5, z = 2/3, w = -9/5
b) x = 3/5, y = 2/3, z = -9/5, w = 9/4
c) x = 9/4, y = 2/3, z = 3/5, w = -9/5
d) x = 2/3, y = 3/5, z = 9/4, w = -9/5

1 Answer

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Final answer:

To find the solution to a system of equations from an augmented matrix in row-echelon form, substitute the given values into the linear equations represented by the matrix to verify consistency. Without the matrix, the correct set of values cannot be determined.

Step-by-step explanation:

To find the solution to a system of equations represented by the augmented matrix in row-echelon form, you would typically back-substitute starting from the last row (assuming the system is consistent and has a unique solution). Looking at the options provided: (a) x = 9/4, y = 3/5, z = 2/3, w = -9/5, it's necessary to check if these values satisfy all the equations obtained from the row-echelon form. If you have the specific augmented matrix, you can plug these values into the equations to verify if they are consistent. Unfortunately, without the actual matrix or equations, we cannot conclude which option is correct. Make sure each value of x, y, z, and w satisfies all the linear equations derived from the matrix.

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