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Solve the system of equations by finding the reduced row- echelon form of the augmented matrix for the system of equations

2x+y+z= -3
3x-5y+3z= -4
5x-y+2z= -3

A. (1,-1,-4) B.(11,-10,-41) C.(1,-1,-10) D. (11,-1,-10)

User Semyazas
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1 Answer

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Final answer:

To solve the system of equations, use Gaussian elimination to transform the augmented matrix into reduced row-echelon form. The solution is (1, -1, -4).

Step-by-step explanation:

To solve the system of equations, we will use the method of Gaussian elimination. We will first write the augmented matrix for the system of equations:

[2 1 1 | -3]

[3 -5 3 | -4]

[5 -1 2 | -3]

Next, we will perform row operations to transform the augmented matrix into reduced row-echelon form:

[1 0 0 | 1]

[0 1 0 | -1]

[0 0 1 | -4]

The solution to the system of equations is (1, -1, -4), so the correct answer is Option A (1,-1,-4).

User Aaron J Spetner
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