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Linear Algebra

Linear Approximation

Find the linear approximation of the function below at the indicated point. (see attached)

Manipulating Basic Linear Equations

The following is offered as a solution of the equation -4[x-2(2x-3)]+1= 1/2(4x-6) -4[x-2(2x-3)]+1=8x-12 -4x-4x+6+1=8x-12 -8x+7=8x-12 7= -12 Because 7 = -12 is not a true equation, the equation has no solution. If this is correct, state that there is no solution. If not, explain in detail why it is not correct

System of Linear Equations

(1.) x-y+2z=13 2x+xy-z=-6 -x+3y + z =-7 a. Provide a coefficient matrix corresponding to the system of linear equations. b. What is the inverse of this matrix? c. What is the transpose of this matrix? d. Find the determinant for this matrix. (2) A = [2 -3] [-4 1] [7 4] and B=[ 6 5]

Matrices, Inverse, Transpose, Determinant, Gaussian Elimination and Cramer's Rule

Matrix methods can be used to solve linear programming problems. A linear programming problem is used to find an optimal solution, subject to stated restraints. 1. For example, consider an accountant who prepares tax returns. Suppose a form 1040EZ requires $12 in computer resources to process and 22 minutes of the accountant'

Word Problems Involving Linear Equations in Two Variables

1. Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city. a) The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floo

Modeling with Linear Equations

There was several questions ask from my algebra class as a homework which I am having difficulty answering. Please help me solve for them thanks. The equation y = 1.13x + 7.85 represents the average monthly cost in dollars for cable television where x represents the number of years after 1980. Use this equation to answer the

Show that f is proper if and only if f* is continuous

Let X and Y be locally compact Hausdorff spaces. Let X* and Y* be their one point compactifications. Let f be a continuous map from X to Y. Let f* be the map from X* to Y* whose restriction to X is f, and which takes the point at infinity in X* to the point at infinity in Y*. Show that f is proper if and only if f* is contin

Solving Systems of Equations

1. y-2x=0 y=8x-9 What is the solution of the system of equations? (i need graph also) 2. r-6s=0 9r-8s=230 What is the solution of the system? 3. x+y= -13 9x+y= -61 What is the solution of the system? 4. (1,2); 6x-5y= -4 2x-7y= -12 is the given ordered pair a solution of the s

Linear Algebra

Linear Algebra Transpose. Please show each step of your solution. Thank you. Suppose that A is invertible....

Linear Algebra : Subspaces

Please show each step of your solution. Thank you. a. Let U and V be subspaces of R^n. Define the intersection of U and V to be U n V = {x E R^n : x E U and x E V}. Show that U n V is a subspace of R^n. Give two examples. b. Is U u V = {x E R^n : x E U or x E V} a subspace of R^n? Give a proof or counterexample.

Linear Algebra : Solving Ax=b

Linear Algebra. The Material is from INVERSE MATRICES. Please explain each step of your solution and check your typos. Thank you.

Word Problems and Systems of Equations

Train Tickets At the the Pittsburg zoo, children ride a train for 25 cents, adults pay $1.00, and Senior citizens 75 cents. On a given day, 1400 passengers paid a total of $740 for the rides. There were 250 more children riders than all other riders. Find the number of children, adult, and senior riders. Manufacturing St

Algebra : Word Problems and Systems of Equations

Rowing Speed: Hank can row a boat 1 mi upstream (against the current) in 24 min. He can row the same distance downstream in 13min. If both the rowing speed and current speed are constant, find Hank's rowing speed and the speed of the current. Airplane Speed - An airplane flying with the wind from Los Angeles to New York Ci

Systems of Equations and Inequalities Word Problems

Statistics. After reading an article on the front page of The New York Times titled "You Have to Be Good at Algebra to Figure Out the Best Deal for Long Distance," Rafaella De La Cruz decided to apply her skills in algebra to try to decide between two competing long-distance companies. It was difficult at first to get the compan

Forty six questions related to finding factors, prime numbers, Greatest common factor, Least common factor, fractions, mathematical operations, solving linear equations, coordinate geometry, graphing, slope intercept form of graphs, inequality graphs, solving a system of equations and word problems.

Complete and please show all the work. Please see attached file for full problem description. 1. List all the factors of 45. 2. Which number is prime? A) 1 B) 12 C) 31 D) 99 3. List all the prime numbers between 25 and 60. 4. Find the GCF for 68, 85, and 153. 5. Find the LCM for 18 and 27. 6. Mul