math 79 linear algebra

Question 1,1.2.3 HW Score: 0%, 0 of 15 points Part 10f 3 Q Points: 0of 1 Row reduce the matrix to reduced echelon form. Identify the pivot positions in the final matrix and in the original matrix, and list the pivot columns 12 3 4 56 7 8 8910 1 Row reduce the matrix to reduced echelon form and identify the pivot positions in the final matrix. The pivot positions are indicated by bold values. Choose the correct answer below O A. O B. Oc. OD. 10 -1 -2 1001 1200 1000 01 2 3 0105 0015 0100 00 0 O 0018 0000 0011 Question 2, 1.2.7 HW Score: 0%, 0 of 15 points O Points: 0 of 1 Save Find the general solution of the system whose augmented matrix is given below. 42 2 3 12 2 -6 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. xq = O B. X1 = X2 is free X, = X2 = X2 = O C. Xq = O D. The system has no solution. Xz IS free X3 is freeQuestion 3, 1.2.11 HW Score: 0%, 0 of 15 points O Points: 0 of 1 Save Find the general solution of the system whose augmented matrix is given below. 3 -7 50 6 - 14 10 0 9 - 21 15 0 Choose the correct answer below. O A. O B. O c. OD. Xy = - 3X2 7 5 X1 = 3 The system has no solutions. X1 = 3 X2 - 3X3 X2 = 7X3 X2 = - 7 X3 is free X, IS free X3 = 5 X3 is freeHW Score: 0%, 0 of 15 points Q Points: 0 of 1 Question 4, 1.2.35 Suppose a 3 x 8 coefficient matrix for a system has three pivot columns. Is the system consistent? Why or why not? Choose the correct answer below. () A. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have nine columns, could have a row of the form [ 000000O00O0A1 ] so the system could be inconsistent O B. Thereis a pivot position in each row of the coefficient matrix. The augmented matrix will have nine columns and will not have a row of the form [ 0O0000O0O0OD0A1 } so the system is consistent. () C. There is at least one row of the coefficient matrix that does not have a pivet position. This means the augmented matrix, which will have nine columns, must have a row of the form [ 000000O0DO0A1 } so the system is inconsistent. OD. Thereisa pivot position in each row of the coefficient matrix. The augmented matrix will have four columns and will not have a row of the form [ 0001 ] so the system is consistent Question 5, 1.2.36 HW Score: 0%, 0 of 15 points O Points: 0 of 1 Save Part 1 of 4 Suppose a system of linear equations has a 3 x5 augmented matrix whose fifth column is not a pivot column. Is the system consistent? Why or why not? To determine if the linear system is consistent, use the portion of the Existence and Uniqueness Theorem, shown below. A linear system is consistent if and only if the rightmost column of the augmented matrix a pivot column. That is, if and only if an echelon form of the augmented matrix has of the form [o .. 0 b with b nonzero.Question 6, 1.2.37 HW Score: 0%, 0 of 15 points O Points: 0 of 1 Save Suppose the coefficient matrix of a system of linear equations has a pivot position in every row. Explain why the system is consistent. Choose the correct answer below. O A. The system is consistent because the rightmost column of the augmented matrix is not a pivot column. O B. The system is consistent because all the columns in the augmented matrix will have a pivot position. O C. The system is consistent because the augmented matrix is row equivalent to one and only one reduced echelon matrix. O D. The system is consistent because the augmented matrix will contain a row of the form | 0 --. 0 b with b nonzero.HW Score: 0%, 0 of 15 points Question 7, 1.2.40 o What would need to be known about the pivot columns in an augmented matrix in order to know that the linear system is consistent and has a unique solution = s E E | x, X Insert Formula Ic o I~ (1 1} it Ml i il " I Clear all