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Gaussian Elimination - 3

X + Y + Z = Equation 1

X + Y + Z = Equation 2

X + Y + Z = Equation 3

HOW TO USE: Simply enter new numbers.

To validate your answer substitute the values of x, y, and z to your original equation 1 , equation 2, and equation 3. The answer must satisfy all the equations or with very small error.

Answer, X = Answer, Y = Answer, Z =

Result of Pivot 1, which means making column 1 = [ 1, 0, 0 ]

Result of Pivot 1, eliminating and in column 1.

X + Y + Z = Equation 1

X + Y + Z = Equation 2. Eliminating

X + Y + Z = Equation 3 . Eliminating

Result of Pivot 2, which means making column 2 = [ CY, 1, 0 ] where C is the constant of Y.

Result of Pivot 2 eliminating in equation 3 above.
Then converting in equation 2 to one (1) in column 2.

ANSWER: 1 Z = .
Using back substitution , substitute Z = in equation 2 below, you will get Y = .
Finally substitute Z = , Y = in equation 1 below, you will get X = .

X + Y + Z = Equation 1

X + Y + Z = Equation 2

X + Y + Z = Equation 3

Important definition to remember about row echelon. The process of reducing augmented matrix in row echelon form is called Gaussian elimination

1. The first nonzero entry in each row is always 1
2. A row with more leading zero entries compare to the previous row must be located below.
3. A row with all zero entries must be below the rows having nonzero entries. Gaussian elimination will not work properly if one of the definition is violated.

Operation 1 - The order in which any two equations are written may be interchanged. Operation 2 - Both sides of the equation may be multiplied by the same nonzero real number. Operation 3 - A multiple of one equation may be added to another equation.

Using Wolfram Alpha to solve three simultaneous linear equations:

x - 3 y + z = 2, 3 x - 4 y + z = 0, 2 y - z = 1

3 x + 2 y - z = 1, 2 x - 2 y + 4 z = -2, -x + 0.5 y -z = 0

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How can IN-V-BAT-AI be used in classrooms ?

The IN-V-BAT-AI solution can be a valuable tool in classrooms, enhancing both teaching and learning experience. Here are some ways it can be utilized:

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⋆ Bridging Learning Gaps : It addresses learning loss by providing consistent access to educational materials, ensuring that students who miss lessons can catch up effectively.

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⋆ Stress Reduction : By alleviating the pressure of memorization, students can focus on understanding and applying concepts, fostering a deeper engagement with the material.

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