Gaussian Elimination Method Example Problem 1

#snsinstitutions #snsdesignthinkers #designthinking #snsctaerospace Gaussian Elimination Method Example Problem 1. Write the system of linear equations in augmented matrix form. The coefficients of the variables are written in the left-hand side of the vertical line, and the constants are written in the right-hand side. 2. Start with the first row of the augmented matrix, and use elementary row operations to eliminate the coefficient of the variable in the first column of the matrix in all the rows below the first row. The goal is to obtain a matrix where the first column has zeros below the first row. 3. Move to the second row and repeat the process, using elementary row operations to eliminate the coefficient of the variable in the second column of the matrix in all the rows below the second row. The goal is to obtain a matrix where the first two columns have zeros below the first two rows. 4. Continue this process until all the columns except the last one have been reduced to zeros below the corresponding diagonal element. 5. The resulting matrix is in upper triangular form. Use back substitution to solve for the variables starting from the last row. 6. Check the solution by substituting the values obtained into the original equations to ensure they hold true.