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Using Gaussian Elimination
To solve 6 - simultaneous linear equations




U + V + W + X + Y + Z = Equation 1

U + V + W + X + Y + Z = Equation 2

U + V + W + X + Y + Z = Equation 3

U + V + W + X + Y + Z = Equation 4

U + V + W + X + Y + Z = Equation 5

U + V + W + X + Y + Z = Equation 6

Using back substitution to find value of U, V, W, X,Y and Z

Answer, U = Answer, V = Answer, W = Answer, X = Answer, Y = Answer, Z =

Result of Gaussian elimination

U + V + W + X + Y + Z = Equation 1

U + V + W + X + Y + Z = Equation 2

U + V + W + X + Y + Z = Equation 3

U + V + W + X + Y + Z = Equation 4

U + V + W + X + Y + Z = Equation 5

U + V + W + X + Y + Z = Equation 6

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.

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