math 79 linear algebra

Question 8, 1.2.43 HW Score: 0%, 0 of 15 points Save O Points: 0 of 1 A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be consistent? Illustrate your answer with a specific system of three equations in two unknowns. Choose the correct answer below. O A. No, overdetermined systems cannot be consistent because there are no free variables. O B. Yes, overdetermined systems can be consistent. For example, the system of equations below is For example, the system of equations below has no solution. consistent because it has the solution X1 = 2, X2 = 4, X1 + X2 = 24 (Type an ordered pair.) X 1 = 2, X2 = 4, X 1 + X2 = 8 O C. No, overdetermined systems cannot be consistent because there are fewer free variables than O D. Yes, overdetermined systems can be consistent. For example, the system of equations below is equations. For example, the system of equations below has no solution. consistent because it has the solution X1 = 2, X2 = 4, X1 + X2 = 12 (Type an ordered pair.) X1 = 2, X2 = 4, X1 + X2= 6L 1l Question 9, 1.2.22 HW Score: 0%, 0 of 15 points QO Points: 00f 1 Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system 1 h 5 -312 -20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice O 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.) O 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 ) (O 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. HW Score: 0%, 0 of 15 points QO Points: 0of 1 Question 10, 1.2.25 Determine whether the statement below is true or false. Justify the answer. In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations Choose the correct answer below. () A. The statement is true. It is possible for there to be several different sequences of row operations that row reduce a matrix. () B. The statement is false. For each matrix, there is only one sequence of row operations that row reduces it () C. The statement is true. The echelon form of a matrix is always unique, but the reduced echelon form of a matrix might not be unique () D. The statement is false. Each matrix is row equivalent to one and only one reduced echelon matrix. HW Score: 0%, 0 of 15 points Q Points: 0of 1 Question 11, 1.2.26 Determine whether the statement below Is true or false. Justify the answer. The echelon form of a matrix is unique. Choose the correct answer below. () A. The statement is true_ Both the echelon form and the reduced echelon form of a matrix are unique. They are the same regardless of the chosen row operations. () B. The statement is false. The echelon form of a matrix is not unique, but the reduced echelon form is unique. () C. The statement is false. Neither the echelon form nor the reduced echelon form of a matrix are unigue. They depend on the row operations performed. () D. The statement is true. The echelon form of a matrix is always unique, but the reduced echelon form of a matrix might not be unique HW Score: 0%, 0 of 15 points QO Points: 0of 1 Question 12, 1.2.27 Determine whether the statement below is true or false. Justify the answer. The row reduction algorithm applies only fo augmented matrices for a linear system. Choose the correct answer below. () A. The statement is false. It is possible to create a linear system such that the row reduction algorithm does not apply to the corresponding augmented matrix. () B. The statement is true. The row reduction algorithm is only useful when it is used ta find the solution of a linear system. () C. The statement is false. The algorithm applies to any matrix, whether or not the matrix is viewed as an augmented matrix for a linear system (0 D. The statement is true. Every matrix with at least two columns can be interpreted as the augmented matrix of a linear system. HW Score: 0%, 0 of 15 points O Points: 0 of 1 Question 13, 1.2.28 Determine whether the statement below is true or false. Justify the answer. The pivot positions in a matrix depend on whether row interchanges are used in the row reduction process. Choose the correct answer below. () A. The statement is true. Every pivot position is determined by the positions of the leading entries of a matrix in reduced echelon form () B. The statement is false. The pivot positions in a matrix are determined completely by the positions of the leading entries in the nonzero rows of any echelon form obtained from the matrix () C. The statement is true. The pivot positions in a matrix are determined completely by the positions of the leading entries of each row which are dependent on row interchanges () D. The statement is false. The pivot positions in a matrix depend on the location of the pivot column. L Y HW Score: 0%, 0 of 15 points Q Points: 0 0f 1 Determine whether the statement below is true or false. Justify the answer. A basic variable in a linear system is a variable that corresponds to a pivot column in the coefficient matrix. Choose the correct answer below. () A. The statement is false. A variable that corresponds to a pivot column in the coefficient matrix is called a free variable, not a basic variable. () B. The statement is false. Not every linear system has basic variables. () C. The statement is true It is the definition of a basic variable (0 D. The statement is true. If a linear system has both basic and free variables, then each basic variable can be expressed in terms of the free variables HW Score: 0%, 0 of 15 points Q Points: 0 of 1 Question 15, 1.2.30 Determine whether the statement below is true or false. Justify the answer. Reducing a matrix to echelon form is called the forward phase of the row reduction process. Choose the correct answer below. () A. The statement is false. Reducing a matrix to echelon form is called the backward phase and reducing a matrix to reduced echelon form is called the forward phase. () B. The statement is true. The forward phase occurs when a linear system has both basic and free variables, which can only be determined by reducing a matrix to echelon form () C. The statement is false. The forward phase does not depend on whether a matrix is in echelon form or reduced echelon form. () D. The statement is true. Reducing a matrix to echelon form is called the forward phase and reducing a matrix to reduced echelon form is called the backward phase