Homework Question. Please answer question 1-7. All parts

Q1. System of Linear Equations

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. E) Select the correct choice below and. if necessary, ll in the answer boxes to complete your choice. . The solution has innitely many elements. . The solution set is empty. - The solution set contains one solution: ( , , , ). (Type integers or simplied fractions.) Find the elementary row operation that transforms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first. - 4 3 0 - 4 3 0 0 2 -2 4 0 2 - 2 4 5 - 2 3 -5 0 18 -12 -5 . . . Find the elementary row operation that transforms the first matrix into the second. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Scale row 3 by (Type an integer or a simplified fraction.) O B. Replace row 3 by its sum with times row 1. (Type an integer or a simplified fraction.) O C. Replace row 3 by its sum with times row 2. (Type an integer or a simplified fraction.) O D. Interchange row 3 and row 2.Find the general solution of the system whose augmented matrix is given below. 1248 3679 E) Select the correct choice below and, if necessary, ll in any answer boxes to complete your answer. A. cj'j: B. l'._. X1 = _ X1 = x2 = x2 is free x3 = x3 = (Use integers or fractions for any numbers in the equation.) (Use integers 0" fractions for any numbers in the equation.) C? C. x1 = C) D. The system has no solution. x2 is free x3 is free (Use integers or fractions for any numbers in the equation.) Find the general solution of the system whose augmented matrix is given below. 01-43 1-1-13 S Select the correct choice below and, if necessary, ll in any answer boxes to complete your answer. '33:? A- _ {I} B. _ x1 x1 ' x2 = X2 = x3 is free x3 = (U59 integers 0" fractions for any numbers in the equation.) (Use integers or fractions for any numbers in the equation.) '32:? C. x _ '12:} D. The system has no solution. 1 _ x2 is free x3 is free (Use integers or fractions for any numbers in the equation.) Find the general solution of the system whose augmented matrix is given below. 1-90-1 0-7 0 10 0-5 4 0 00 1 4 7 0 00 0 0 0 A:} Select the correct choice below and, if necessary, ll in the answer boxes to complete your answer. GA QB @Q u x1 = x1 = x1 =|:| The system is inconsistent. X2 = x2 = x2 is free x3 is free x3 is free x3 = D X4 = x4 = x4 is free x5 is free x5 = x5 is free Determine the value(s) of h such that the matrix is the augmented matrix of a consistent linear system. 1h 4 -26-12 (I) Select the correct choice below and, if necessary, ll in the answer box to complete your choice. A- The matrix is the augmented matrix of a consistent linear system if h #5 (Use a comma to separate answers as needed. Type an integer or a simplified fraction.) '17-?\" 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. Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. X1 + hx2 = 5 4x1 + 12X2 = k . . . a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.) O A. The system has no solutions only when h # and k is any real number. O B. The system has no solutions only when k # and h is any real number. O C. The system has no solutions only when h # and k = O D. The system has no solutions only when h = and k is any real number. O E. The system has no solutions only when h = and k # OF. The system has no solutions only when h # and k # O G. The system has no solutions only when h = and k = O H. The system has no solutions only when k = and h is any real number