Solve the system by using elementary row operations on the equations. Follow the systematic elimination procedure. 5x1 + 10x2 = 20 4x1 + 5x2 = 22 Find the solution to the system of equations. (Simplify your answer. Type an ordered pair.)
Find the point (x1, x2) that lies on the line x1 + 2x2 = 11 and on the line x1 - x2 = -1. See the figure. The point (x1, x2) that lies on the line x1 + 2x2 = 11 and on the line x1 - x2 = -1 is (Simplify your answer. Type an ordered pair.)
The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The solution set contains one solution (Type integers or simplified fractions.) B. The solution set has infinitely many elements. C. The solution set is empty.
4. The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. Select the correct choice below and if necessary fill in the answer boxes to complete your choice. (A) The solution is empty. (B) The solution set contains one solution (Type integers or simplified fractions). (C) The solution has infinitely many elements.
Solve the system x1 - 3x3 = 6 2x1 + 4x2 + 7x3 = 11 2x2 + 4x3 = 2 Select the correct choice below and if necessary fill in the answer boxes to complete your choice. (A) The unique solution of the system is (Type integers or simplified fractions) (B) The system has infinitely many solutions (C) The system has no solution
Determine if the given system is consistent. Do not completely solve the system. 3x1 + 6x3 = 12 x2 - 4x4 = 4 -2x2 + 6x3 + 3x4 = 4 6x1 + 9x4 = -2 Choose the correct answer below. A. The system is inconsistent because the system cannot be reduced to a triangular form. B. The system is consistent because the system can be reduced to a triangular form that indicates that no solutions exist C. The system is inconsistent because the system can be reduced to a triangular form that contains a contradiction. D. The system is consistent because the system can be reduced to a triangular form that indicates that a solution exists
Do the three lines 2x1 - 4x2 = 15, 4x1 + 6x2 = -54, and -2x1 - 10x2 = 69 have a common point of intersection? Explain. Choose the correct answer below. A. The three lines have at least one common point of intersection. B. The three lines do not have a common point of intersection. C. There is not enough information to determine whether the three lines have a common point of intersection.
Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrix is the augmented matrix of a consistent linear system if h = (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) B. The matrix is the augmented matrix of a consistent linear system if h =/ (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) C. The matrix is the augmented matrix of a consistent linear system for every value of h. D. The matrix is not the augmented matrix of a consistent linear system for any value of h.
Every elementary row operation is reversible. Determine whether the statement below is true or false. Justify the answer. Choose the correct answer below. A. The statement is false. The only reversible row operation is interchanging two rows. B. The statement is true. Interchanging can be reversed by scaling, and scaling can be reversed by replacement. C. The statement is true. Replacement, interchanging, and scaling are all reversible. D. The statement is false. The only reversible row operations are scaling a row and interchanging two rows.
Elementary row operations on an augmented matrix never change the solution set of the associated linear system. Determine whether the statement below is true or false. Justify the answer. Choose the correct answer below. A. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, scaling a row by a nonzero constant can change the solution set of that system. B. The statement is true. Each elementary row operation replaces a system with an equivalent system. C. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found. D. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, replacing one row by the sum of itself and a multiple of another row can change the solution set of that system.