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    Linear Algebra

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    Systems of Equations Word Problems

    A child in an airport is able to cover 380 meters in 4 minutes running at a steady speed down a moving sidewalk in the direction of the sidewalk's motion. Running at the same speed in the direction opposite to the sidewalk's movement, the child is able to cover325 meters in 5 minutes. What is the child's running speed on a sti

    Systems of Equations Word Problems

    In a family there are two cars. In a given week, the first car gets an average of 40 miles per gallon, and the second car gets 25 miles per gallon. The two cars combined drive a total of 1775 miles in that week, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?

    Systems of Equations Word Problems: Tickets Sold

    A total of 200 tickets were sold for the carnival to adults and children. Children tickets were $6 and adult tickets were $8. If the total revenue for the carnival is $550 dollars, then how many tickets of each type were sold?

    Find the linear equation.

    56. If you earned an average of $25,000 over your working life and you retire after 2005 at age 62, 63, or 64, then your annual Social Security benefit will be $7,000, $7500, or $8000 respectively (www.ssa.gov). There is a linear equation that gives the annual benefit b in terms of age a for these three years. Find the equation.

    Systems of Linear Inequalities

    1) What conditions need to be satisfied for a solution of a system of linear inequalities to have it's solution in the first quadrant? Create an example of such a system. 2) Can you give a real world example when the solution of a system of inequalities must be in the first quadrant? 3) Suppose, wheat and sugar are two b

    Linear Regression Equations : 3 Equations, 3 Unknowns

    How do you go mathamatically from eq. 12.4 to eq. 12.5 when solving three equations with three unknowns given the summation rules on page 460? Please show all steps of the mathamatical work by hand without using any computer programs

    Solving Linear Algebra Problems

    Let n be the set of natural numbers let i and j be seg n Show that det(t sub i, subj (In)) = -1 Where t sub i, subj means transpose any two rows in the identity matrix (In)

    Show that every tree is central or bicentral.

    1.- A tree is central if its center is K1 and bicentral if its center is K2. Show that every tree is central or bicentral. ( Kn is call complete graph and it if every two of its vertices are adjacent and every vertex has degree n) 2.- Prove taht a tree with Delta(T)=k ( Delta means maximum degree) has at least k vertices of d

    Order and neighbors

    For an integer n, define the graph Tn as follows: Vertices are 2-element subsets of {1,2,...,n}. Two vertices are adjacent if they have one element in common. (a) What are the order and the size of this graph? (b) How many neighbors does each vertex have? (c) Draw T5.

    Probs in Linear Algebra

    1 3 11. Consider (A) = 2 1 (a) Find the eigenvalue and corresponding eigenvectors of A. (b) Determine matrices B and C such that B A C is diagonal. (c) Show the eigenvectors of (A) are linearly independent. (d) Repre

    Solve each system by the substitution method.

    Solve each system by the substitution method. Indicate whether each system is INDEPENDENT, INCONSISTENT or DEPENDENT 1. x+3(y-1)= 11 2(x-y)+8y+28 2. 1/3x-1/6y+1/3 1/6x+1/4y=0 Solve each compound inequity. State the solution set using interval notation and graph it. 3. x <=0 and x+6>3 and 1/4x>3 4. 1/3x>

    Logical Equivalence

    2. Find the sum: 2+4 +6+...+2n. (Hint: you can use induction) 3. Arc the following statements logically equivalent? (a) ~(pÙ¨q) and (~pV~q) (b) ~(pVq) and (~pÙ¨~q) (e) (A U B)c and Ac &#8745; Bc (remember: Ac denotes the complement of the set A)

    linear equations and inequality

    Complete each problem show work and ad graphs as needed John spent 1/3 of his inheritance on loose women, 1/5 on expensive cigars, and 3/10 on liquor. He invested the rest in lottery tickets. What percent of his inheritance went to lottery tickets? Evaluate the expression: -(2 - 3)4 Fred and Ethel are florists. They a

    Solving Linear Systems of Equations

    1. INDEPENDENT LINEAR SYSTEM a. a system with exactly one solution b. an equation that is satisfied by every real number c. equations that are identical d. a system of lines 2. DEPENDENT SYSTEM a. a system that is independent b. a system that depends on a variable c. a system that has no soluti

    Solving Systems of Linear Equations by the Echelon Method

    4. solve by gauss jordan method. 28.6x + 94.5y + 16.0z - 2 .94w = 198.3 16.7x + 44.3y - 27.3z + 8.9w = 254.7 12.5x - 38.7y +92.5z +22.4w =562.7 40.1x - 28.3y + 17.5z - 10.2w = 375.4 5. Solve by echelon method 4x - y + 3z = -2 3x + 5y - Z =15 -2x+y + 4z = 14 6. Solve the system of equation...let z be the

    Exact and appropriate solutions

    Find exact and appropriate solutions to the problem. Find two positive real numbers that differ by 1 and have a product of 1.

    Equal Interval Notation

    Write the sets below using interval notation. If the set is empty, write 0 . (a) {y|y> or equal to -2 and y > or equal to 1 } (b) CUD, where C = {y|y>0} D = {y|y>3} where and

    Solving Linear Systems of Equations

    For each system of linear equations.classify the system as "consistent dependent," "consistent independent," or "inconsistent," and tell whether this makes it a unique solution, no solution, or infinately many solutions. 1) Line 1: y=-x + 2 Line 2: y=1/2 x + 2 2) Line 1:y=-2x + 2 Line 2: 2x + y=2 3) Line 1: y=

    Level Curves

    Sketch the graph: z= f(x,y) where f(x,y)= x^2 + xy ; c=0,1,2,3,-1,-2,-3 Please show/describe all steps AND explain why it is a hyperbola. Also, sketch the graph: z=f(x,y) where f(x,y)= x/y ; c= 0,1,2,3,-1,-2,-3 Please show/describe all steps.

    Probability and Solving Systems of Equations

    1. A coin is tossed and a die is rolled. What is the probability that the coin shows heads and the die shows a 1 OR a 2? I tried this one and came up with 1/6 but the OR part is kicking my tail. Maybe I am just over thinking this one. 2. A technician is designing a new portable CD player that requires ten batteries fo