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Answer :
Final answer:
The system is put in echelon form by ordering equations from the one containing the highest power of x to the lowest. The correct sequence is 3x^1 - 2x^2 + 7x^3 = 0, followed by -x^2 - 4x^3 = 4, and ending with -2x^3 = -2.
Explanation:
To put a linear system in echelon form, we must arrange the equations in a way that the leading coefficient (the first non-zero number from the left in an equation) of each row is to the right of the leading coefficient of the row above it. Looking at the provided options, we can rearrange the equations to meet this criterion.
For echelon form, we start with the equation that has the variable with the highest power (x^1 or just x) and then proceed with equations involving lower powers of x or the ones with missing x terms. Thus, the correct answer is:
- 3x^1 - 2x^2 + 7x^3 = 0 (This should be the first equation as it contains x, x^2, and x^3)
- −x^2 −4x^3 = 4 (This should be the second equation, as it contains only x^2 and x^3, and follows an equation with x^1)
- −2x^3 = −2 (This should be the last equation, as it contains only x^3)
Therefore, the correct answer that represents the system in echelon form is:
C) 3x^1 - 2x^2 + 7x^3 = 0, -x^2 - 4x^3 = 4, -2x^3 = -2
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