### Linear Algebra : Four Fundamental Subspaces

Please see the attached file. Please show each step of your solution. Thank you.

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Please see the attached file. Please show each step of your solution. Thank you.

Please show each step of you solution. Thank you.

1) Use inductive reasoning to determine the next three numbers in the pattern: 3,12,26,45.....? (I don't seem to find a pattern?) 2) Find the counterexample to show that the following statemnet is incorrect. "the sum of any odd numbers is divisible by 4. ( I tried several odd numbers and the answer is always divisible by 4)

Seven practice problems are in the attached file.

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

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

The material is from ABSTRACT VECTOR SPACE. Please kindly show each step of your solution. Thank you.

(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]

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'

From "The four fundamental subspaces". Please show each step of your solution.

Prove that pivot columns of matrix A form a basis for C(A). From "The Four Fundamental Subspaces". Please show each step of your solution.

Attached are problems involving linear equations. Thank you for your help. 1.) The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring

The material is from Basis and Dimension. Please see the attached file for the fully formatted problems.

The material is from Linear Independence. Please show each step of your solution. Thank you.

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

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

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

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

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.

Let A be an nxn matrix. Verify that: V = { x E R^n : Ax = 3x} is a subspace of R^n.

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

Please see the attached file for the fully formatted problems. (Please solve for parts (a) and (d).)

For each of the following equations, explain why it is or is not linear. a. 2X - 3Y > 12 b. X2 + Y2 < 100 c. 1.5X - XY > 0 d. 1500X + 200Y + 1000Z > 7500 e. 2000X ≥ 1500Z + 750

Please see the attached file for the fully formatted problems.

Please explain each step of your solution. Thank you.

Please explain each step of your solution. Thank you.

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

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

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