4A Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) Find the result of performing the elementary row operation R 3 + (5) R 2 on the system 1 0 3 9 0 1 -3 2 . 0 -5 4 1 1) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1 2) The system 0 1 A) 1 0 0 0 1 -3 0 1 -3 0 0 -2 1 3 5 is equivalent to the system 1 -3 4 B) C) -2 1 0 0 -2 1 0 0 -2 . . 5 0 1 -3 5 0 1 3 5 . 4 0 0 0 4 0 1 -3 6 2) D) 1 0 0 -2 0 3 -9 5 . 1 1 -3 4 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the indicated row operation to change the matrix. 3) Replace R 2 by 1 R 1 + 1 R 2. 3 2 3) 3 0 12 -2 4 6 Use the Gauss-Jordan method to solve the system of equations. 4) 3x + 5y = 16 3x = -9 5) 4) 5) x - y + 4z = -6 5x + z = -1 x + 3y + z = 5 6) Pivot the matrix 1 3 about the element 3. 4 -2 6) Solve the system of linear equations using the Gaussian elimination method. If there is no solution, state so; if there are infinitely many solutions, find two of them. 7) 7) x - y + 2z = 2 y - 2z = 1 -3x + 5y - 10z = -4 1 8) 8) x - y - 2z = 2 y - 2z = 1 -3x + 5y - 10z = -4 For the system of equations, state whether there is one, none, or infinitely many solutions. If there are one or more solutions, give all values of x, y, and z that satisfy the system. 9) 9) x+y- z = 1 y - 2z = 1 x+y- z = 2 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. x - y = 7 . Which of the following statements is true? 2x - 2y = k A) If k = 10, the system has infinitely many solutions. B) If k = 10, the system has no solution. C) If k 10, the system has exactly one solution. D) none of these 10) Consider the system: 10) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Gauss-Jordan method to solve the system of equations. 11) -4x - 2y = 6 -16x - 8y = -1 11) Perform the matrix operation. 12) Let A = 1 3 and B = 0 4 2 6 -1 6 . Find 4A + B. 12) . Find C - 4D. 13) 1 13) Let C = -3 2 and D = -1 3 -2 Find the matrix product AB, if it is defined. 14) A = -1 3 , B = -2 0 . 2 2 -1 4 15) A = 3 -2 1 0 4 -2 16) A = 1 3 -2 2 0 3 , B= 4 0 -2 3 3 0 , B = -2 1 0 3 14) . 15) . 16) 2 17) Write the system of linear equations as a matrix equation. x + 2y + 3z = 4 6y + 7z = 8 x = 5 Write the matrix equation as a system of linear equations without matrices. 18) -7 0 -8 x1 = 1 1 8 x2 -8 -5 -7 3 17) 18)