Example Find the line of intersection of the planes 3 x 2 y z 1 and 2 x y 4 z 5

# Example find the line of intersection of the planes 3

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Example : Find the line of intersection of the planes 3 x + 2 y + z = - 1 and 2 x - y + 4 z = 5.
§ 1.1 and § 1.2 1.24 Gauss-Jordan Elimination Definition (1) Write the augmented matrix of the system of linear equations. (2) Use elementary row operations to reduce the augmented matrix to reduced row echelon form. (3) If the resulting system is consistent, solve for the leading variables in terms of any remaining free variables. Example : Find the line of intersection of the planes 3 x + 2 y + z = - 1 and 2 x - y + 4 z = 5. [ A | b ] = 3 2 1 - 1 2 - 1 4 5
§ 1.1 and § 1.2 1.24 Gauss-Jordan Elimination Definition (1) Write the augmented matrix of the system of linear equations. (2) Use elementary row operations to reduce the augmented matrix to reduced row echelon form. (3) If the resulting system is consistent, solve for the leading variables in terms of any remaining free variables. Example : Find the line of intersection of the planes 3 x + 2 y + z = - 1 and 2 x - y + 4 z = 5. [ A | b ] = 3 2 1 - 1 2 - 1 4 5 R 2 = 3 R 2 - 2 R 1 -----------→
§ 1.1 and § 1.2 1.24 Gauss-Jordan Elimination Definition (1) Write the augmented matrix of the system of linear equations. (2) Use elementary row operations to reduce the augmented matrix to reduced row echelon form. (3) If the resulting system is consistent, solve for the leading variables in terms of any remaining free variables. Example : Find the line of intersection of the planes 3 x + 2 y + z = - 1 and 2 x - y + 4 z = 5. [ A | b ] = 3 2 1 - 1 2 - 1 4 5 R 2 = 3 R 2 - 2 R 1 -----------→ 3 2 1 - 1 0 - 7 10 17
§ 1.1 and § 1.2 1.24 Gauss-Jordan Elimination Definition (1) Write the augmented matrix of the system of linear equations. (2) Use elementary row operations to reduce the augmented matrix to reduced row echelon form. (3) If the resulting system is consistent, solve for the leading variables in terms of any remaining free variables. Example : Find the line of intersection of the planes 3 x + 2 y + z = - 1 and 2 x - y + 4 z = 5. [ A | b ] = 3 2 1 - 1 2 - 1 4 5 R 2 = 3 R 2 - 2 R 1 -----------→ 3 2 1 - 1 0 - 7 10 17 R 2 : =- R 2 / 7 ---------→ R 1 : = R 1 / 3
§ 1.1 and § 1.2 1.24 Gauss-Jordan Elimination Definition (1) Write the augmented matrix of the system of linear equations. (2) Use elementary row operations to reduce the augmented matrix to reduced row echelon form. (3) If the resulting system is consistent, solve for the leading variables in terms of any remaining free variables. Example : Find the line of intersection of the planes 3 x + 2 y + z = - 1 and 2 x - y + 4 z = 5. [ A | b ] = 3 2 1 - 1 2 - 1 4 5 R 2 = 3 R 2 - 2 R 1 -----------→ 3 2 1 - 1 0 - 7 10 17 R 2 : =- R 2 / 7 ---------→ R 1 : = R 1 / 3 1 2 / 3 1 / 3 - 1 / 3 0 1 - 10 / 7 - 17 / 7
§ 1.1 and § 1.2 1.24 Gauss-Jordan Elimination Definition (1) Write the augmented matrix of the system of linear equations. (2) Use elementary row operations to reduce the augmented matrix to reduced row echelon form. (3) If the resulting system is consistent, solve for the leading variables in terms of any remaining free variables. Example : Find the line of intersection of the planes 3 x + 2 y + z = - 1 and 2 x - y + 4 z = 5.