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Algebra and Trigonometry (MindTap Course List)
- Solve the system of equations using a matrix: {2x5y+3z=83xy+4z=7x+3y+2z=3 .arrow_forwardOne hundred liters of a 50% solution is obtained by mixing a 60% solution with a 20% solution. Use a system of linear equations to determine how many liters of each solution are required to obtain the desired mixture. Solve the system using matrices.arrow_forwardWrite the system of equations that that corresponds to the augmented matrix. 202. [103120012| 1 23]arrow_forward
- Write the augmented matrix of the given system of equations. 4x3y=113x+2y=4arrow_forward(a) Write the following system as a matrix equation AX=B . (b) The inverse of A is (c) The solution of the matrix equation is X=A1B . (d) The solution of the system is x = ____, y = ____.arrow_forwardUse matrix methods to solve each problem Nutritional planning One ounce of each of three foods has the vitamin and mineral content shown in the table. How many ounces of each must be used to provide exactly 22 milligrams mg of niacin, 12 mg of zinc, and 20 mg of vitamin C? Food Niacin Zinc Vitamin C A 1 mg 1 mg 2 mg B 2 mg 1 mg 1 mg C 2 mg 1 mg 2 mgarrow_forward
- Floral Design: A florist is creating 10 centerpieces. Roses cost $2.50 each, lilies cost $4 each, and irises cost $2 each. The customer has a budget of $300 allocated for the centerpieces and wants each centerpiece to contain 12 flowers, with twice as many roses as the number of irises and lilies combined. (a) Write a system of linear equations that represents the situation. Then write a matrix equation that corresponds to your system. (b) Solve your system of linear equations using an inverse matrix. Find the number of flowers of each type that the florist can use to create the 10 centerpieces.arrow_forwardWrite the augmented matrix of the following system of equations. System {x+yz=1x+2z=32yz=3 Augmented matrixarrow_forwardNutrition A nutritionist is studying the effects of the nutrients folic acid, choline, and inositol. He has three types of food available, and each type contains the following amounts of these nutrients per ounce. (a) Find the inverse of the matrix [313424324] and use it to solve the remaining parts of this problem. (b) How many ounces of each food should the nutritionist feed his laboratory rats if he wants their daily diet to contain 10 mg of folic acid, 14 mg of choline, and 13 mg of inositol? (c) How much of each food is needed to supply 9 mg of folic acid, 12 mg of choline, and 10 mg of inositol? (d) Will any combination of these foods supply 2 mg of folic acid, 4 mg of choline, and 11 mg of inositol?arrow_forward
- Determine whether the matrix is in row-echelon form. If it is, determine whether it is in reduced row-echelon form. 1024011130000arrow_forwardCAPSTONE In your own words, describe the difference between a matrix in row-echelon form and a matrix in reduced row echelon form. Include an example of each to support your explanation.arrow_forwardMuseum A natural history museum borrows $2,000,000 at simple annual interest to purchase new exhibits. Some of the money is borrowed at 7%, some at 8.5%, and some at 9.5%. Use a system of linear equations to determine how much is borrowed at each rate given that the total annual interest is $169,750 and the amount borrowed at 8.5% is four times the amount borrowed at 9.5%. Solve the system of linear equations using matrices.arrow_forward
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