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Linear Algebra

Linear Equations Word Problems

In Atlantic City, Nick played the slot machines for 12 h. He lost $45 an hour. Use real numbers to represent the change in Nick's financial status at the end of 12 h. Compose a note explaining how you arrived at the solution. What difficulties (if any) did you encounter?

Dependency Equation, Feasibility Analysis and Row Reduced Echelon Form

4. The Volta Battery Company manufactures AA, A. C, and D batteries in each of four plants. The daily production (in 1000's) for the four plants is given the following table: [TABLE] (a) The vectors that represent the production at the various plants are not linearly independent. Show this and find a dependency equation. (b)

Euclidean Equation and Linearly Indpedendent Set

2. Consider the set S = {(t, 1, 1), (1, 0, 1), (1, 1, 3t)}. (a) What value(s) of t will make the set linearly independent? (1)) Choosinig a value of t that will make S linearly dependent fnd the Euclidean (linear) equation form of the subspace spanned by S.

Linear approximation

A = alpha , B = beta Show that the linear approximation of the function f(x,y) = x^a y^B at (1,1) is x^a Y^B = 1 + a(x-1) + B(y-1) .

Algebra

Please see the attached file for complete description 1. Solve the system by graphing. x + y = 4 -x + y = 2 2. Determine which two equations represent perpendicular lines. 3. Solve the system by graphing. 3x + y = 6 3x - y = 0 4. Graph the inequality y < -3 5. Solve the following system of linear inequalit

General vector spaces - basis and dimension

10. Find the coordinate vector of p relative to the basis S = {p1, p2, p3}. (a) p = 4 - 3x + x2; p1 = 1, p2 = x, p3 = x2 (b) p = 2 - x + x2; p1 = 1 + x, p2 = 1 + x2, p3 = x + x2 22. Find the standard basis vectors that can be added to the set {v1, v2} to produce a basis for R4. v1 = (1, -4, 2, -3), v2 = (-3, 8, -4,

General Vector Spaces - Linear Independence

2. Which of the following sets of vectors in R3 are linearly dependent? a) (4, -1, 2), (-4, 10, 2) b) (-3, 0, 4), (5, -1, 2), (1, 1, 3) c) (8, -1, 3), (4, 0, 1) d) (-2, 0, 1), (3, 2, 5), (6, -1, 1), (7, 0, -2) 4. Which of the following sets of vectors in P2 are linearly dependent? a) 2 - x + 4x2, 3 + 6x + 2x2, 2

Systems of Linear Equations Word Problems

1. Leon drove 270 to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10mph faster than Leon, how fast did each of them drive? 2. A company specializing in magazine sales over the telephone found that in 2500 phone calls, 360 resulted in sales and were made by a male caller, and 480 resulted in sal

Linear Equations:Predicted sales of a company

Suppose the sales of a company are given by S(x) = $200x + $20,000 where x is measured in years and x = 0 corresponds to the year 1996. Find the predicted sales in the year 2002 assuming the trend continues.

Graphing and Solving Systems of Linear Equations

See attached file for full problem description. Graph y = -1. Solve the system by addition or substitution. 3x + 6y = 0 x = Find the slope of the line passing through the points (-4, 10) and (-6, 5). Solve: 6x + 4(3x - 2) = 6x + 2 Graph 3x + y = 3. Let y vary directly with x, with

Linear Equation

(1) Given a line containing the points (1, 4), (2, 7), and (3, 10) determine the slope-intercept form of the equation and provide one additional point on this line, and graph the function.

Subgroups and indexes

Explain what the index of a subgroup and a coset of a group are. Also, prove that if N is a subgroup of a group G such that [G: N] = 2, and if "a" and "b" are elements of G, then the product "ab" is an element of N if and only if either (1) both "a" and "b" are elements of N or (2) neither "a" nor "b" is an element of N.

Linear Equations

Not sure how to solve this particular equation. I am finding linear equations to be a bit confusing. Can you show me how to do this one? dy/dt = y/2 + 4e^t/2

Divergence, Gradients and Eigenvalues

Let psi be an eigenfunction of "div(grad)" + V for a real eigenvalue lambda. Note: Here Psi is not necessarily in L^2 and V is real-valued. If j = 2 Im( psi-bar x grad psi) , then show that div(j) = 0 Also, compute div (j) when lambda is in C/R and then give an example with an explicit V, psi, lambda, j, and div(j)

Linear Operators - Solving Equations Finding Annihilator of a Space

Question (4) Solve the equations over R X1 + 2X2 - 3X3 + 4X4 = 0 X1 + 3X2 - X3 = 0 6X1 + X3 + 2X4 = 0 Question (5) If F = R find Annihilator A(W) of the space W spanned by (2 , 4 , 6 ) , ( 1 , 6 , 2 ). ( Note : Here F is the field and R represents the set of Real Numbers) See attached file for full problem des

Eigenvalues

Find the general solution (determine eigenvalues) of the system x'(t) = Ax(t) See attached file for full problem description.