Homework, Page 604

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Homework, Page 604. Use substitution to solve the system of equations. 1. . Homework, Page 604. Use Gaussian elimination to solve the system of equations. 5. . Homework, Page 604. Perform the indicated elementary row operations on the matrix. 9. . Homework, Page 604.

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Homework, Page 604

Use substitution to solve the system of equations.

1.

Homework, Page 604

Use Gaussian elimination to solve the system of equations.

5.

Homework, Page 604

Perform the indicated elementary row operations on the matrix.

9.

Homework, Page 604

What elementary row operations applied to the matrix will yield the given matrix.

13.

Homework, Page 604

Find a row echelon form for the matrix.

17.

Homework, Page 604

Find the reduced row echelon form for the matrix.

21.

Homework, Page 604

Write the augmented matrix corresponding to the system of equations.

25.

Homework, Page 604

Write the system of equations corresponding to the augmented matrix.

29.

Homework, Page 604

Solve the system of equations by finding a row echelon form for the augmented matrix.

33.

Homework, Page 604

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.

37.

Homework, Page 604

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.

41.

Homework, Page 604

Write the system of equations as a matrix equation AX = B, with A as the coefficient matrix of the system.

45.

Homework, Page 604

Solve the system of equations by using an inverse matrix.

49.

Homework, Page 604

Solve the system of equations by using an inverse matrix.

53.

Homework, Page 604

Use the method of your choice to solve the system of equations.

57.

Homework, Page 604

Use the method of your choice to solve the system of equations.

61.

Homework, Page 604

Use the method of your choice to solve the system of equations.

65.

Homework, Page 604

Determine f so that its graph contains the given points.

69.

Homework, Page 604

73. Children ride a train for 25 cents, adults pay \$1.00, and seniors pay 75 cents. On a given day, 1400 passengers paid \$740 for their rides. There were 250 more children than all other passengers. Find the number of children, adults, and senior riders.

Homework, Page 604

77. Morgan has \$50,000 to invest and wants to receive \$5,000 interest the first year. He puts part in CDs earning 5.75% APY, part in bonds earning 8.7% APY, and the rest in a growth fund earning 14.6% APY. How much should he put in each fund if he puts the least amount possible in the growth fund.

Homework, Page 604

Use inverse matrices to find the equilibrium point for the supply and demand curves.

81.

7.4

Partial Fractions

• Partial Fraction Decomposition
• Denominators with Linear Factors
• Denominators with Irreducible Quadratic Factors
• Applications

… and why

Partial fraction decompositions are used in calculus in

integration and can be used to guide the sketch of the

graph of a rational function.

Homework
• Homework Assignment #12
• Page 614, Exercises: 1 – 49 (EOO), skip 45

7.5

Systems of Inequalities in Two Variables

• Graph of an Inequality
• Systems of Inequalities
• Linear Programming

… and why

Linear programming is used in business and

industry to maximize profits, minimize costs, and to

help management make decisions.

• Draw the graph of the equation obtained by replacing the inequality sign by an equal sign. Use a dashed line if the inequality is < or>. Use a solid line if the inequality is ≤ or ≥.
• Check a point in each of the two regions of the plane determined by the graph of the equation. If the point satisfies the inequality, then shade the region containing the point.
Example Solving a Word Problem

38. Paul’s diet is to contain at least 24 units of carbohydrates and 16 units of protein. Food substance A costs \$1.40 per unit and each unit contains 3 units of carbohydrates and 4 units of protein. Food substance B costs \$0.90 per unit and each unit contains 2 units of carbohydrates and 1 units of protein. How many units of each food substance should be purchased to minimize cost? What is the minimum cost?