1.Find the augmented matrix representing the system of equations. x1 + x2 + x3 = 4 x1 + 3x2 + x3 = 2 x1 + 3x2 + 2x3 = 5 2. Find the augmented matrix representing the system of equations. 2x1 + x2 + 4x3 + 5x4 + 2x5 = 5 x1 + x2 + 5x3 + 3x4 + 3x5 = 2 3. Interpret the row-reduced matrix as the solution of a system of equations. (Enter your answers as a comma-separated list. If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parameter t.) 1 0 0 0 1 0 0 0 1 3 8 6 4. Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix. 0 1 0 1 0 0 3 7 0 0 1 6 5. Use an appropriate row operation or sequence of row operations to find the equivalent row-reduced matrix. 1 0 1 0 1 0 0 0 1 6. Solve the system of equations by the Gauss-Jordan method. (Enter your answers as a comma-separated list. If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parameter t.) x1 + x2 + x3 = 3 x1 + 2x2 + 2x3 = 10 x1 + 3x2 + 2x3 = 15 7. Formulate the situation as a system of linear equations. Be sure to state clearly the meaning of each variable. Solve using the Gauss-Jordan method. State your final answer in terms of the original question. (If the system is inconsistent, answer INCONSISTENT. If the system is dependent, parametrize the solutions in terms of the parameters u and v.) A large commercial farm needs 41,500 pounds of potash, 81,000 pounds of nitrogen, and 29,500 pounds of phosphoric acid. Three brands of fertilizer, GrowRite, MiracleMix, and GreatGreen, are available and contain the amounts of potash, nitrogen, and phosphoric acid per truckload listed in the table. How many truckloads of each brand should be used to provide the required 5 2 9 potash, nitrogen, and phosphoric acid? x1 = truckloads of GrowRite x2 = truckloads of MiracleMix x3 = truckloads of GreatGreen (Pounds per truckload) Grow Rite Miracl eMix GreatGreen Potash 400 600 700 Nitrogen 500 1000 1600 Phosphoric acid 300 400 500 8. Use the given matrix to find the expression. A= 6 9 1 6 2 9 2 3 6 ; At 9. Use the given matrix to find the expression. C= 6 8 6 4 9 5 4 9 7 ; 3C 10.Use the given matrices to find the expression. A= 7 7 7 8 3 8 4 7 4 C= 4 2 9 3 8 3 8 1 9 ; A+C 11. Find the matrix product. 2 3 (5 4) 12. Find the matrix product. 5 4 4 3 3 2 5 3 2 13. Find the matrix product. 3 1 1 3 1 3 1 3 2 3 1 1 14. Rewrite the system of linear equations as a matrix equation AX = B. x1 + 3x2 + 6x3 = 1 x1 + x2 + x3 = 4 3x1 + 6x2 + 2x3 = 8 15. Rewrite the system of linear equations as a matrix equation AX = B. 4x1 + 2x2 3x3 + x4 + 5x5 = 6 x1 + x2 3x3 + x4 + 5x5 = 6 16. Formulate the situation in matrix form. Be sure to indicate the meaning of your rows and columns. Find the requested quantities using the appropriate matrix arithmetic. A sports apparel company manufactures shorts, tee shirts, and caps in Costa Rica and Honduras for importation and sale in the United States. In Costa Rica the labor costs per item are 65 per pair of shorts, 20 per tee shirt, and 40 per cap, while the costs of the necessary materials are $1.60 per pair of shorts, 95 per tee shirt, and $1.15 per cap. In Honduras the labor costs per item are 75 per pair of shorts, 25 per tee shirt, and 50 per cap, while the costs of the necessary materials are $1.50 per pair of shorts, 75 per tee shirt, and $1.10 per cap. Represent these costs as a labor cost matrix L and a materials cost matrix M. Use these matrices to find the total cost matrix C for these products in these countries. (Let the first row represent the cost, in pennies, in Costa Rica and the second row represent the cost, in pennies, in Honduras.) shorts tee shirt cap L = M = C = M C