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Linear Algebra

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

Systems of Linear Equations and Inequalities

1. Solve by substitution: x + y = 6 2x - 4y = 0 2. Does the shaded region of the graph of the system of equations x < 3, x + 7< 4 include the point (2, 3)? How do you know? 3. Explain what it means for a system of equations to be inconsistent and how you can tell whether a system is inconsistent usin

Linear Congruences : Chinese Remainder Theorem

The idea of this problem is to investigate solutions to x2&#8801;1(mod pq) where p and q are distinct odd primes. (a) Show that if p is an odd prime, then there are exactly two solutions modulo p to x2&#8801;1(mod p). (b) Find all pairs (a,b) &#1028; Zp x Zq such that a2&#8801;1(mod p) and b2&#8801;1(mod q). (c) Let p=17 an

Solving Systems of Linear Equations by Substitution

4x+y=12 (1) x-y=8(2) 4x+y=12 x-y=8 5x/5 = 20/5 X=4 4(4) =y - 12 16+y = 12 Y =4 I think this would be an example of elimination method for solving a system of equations however I am unsure how it would transfer to substitution method thus I am needing assistance. I am needing this to be illustrated if you wi

Solving Systems of Equations Word Problems and Gaussian Elimination

1. Jim wants to plan a meal with 169 grams of carbs and 1330 calories. If green beans have 7 grams of carbs and 30 calories per half cup serving and if french fried shrimp have 9 grams of carbs and 190 calories per three ounce serving how many servings of green beens and shrimp should be used? 2. Solve the system of equation

Simple questions

(See attached file for full problem description) --- Section 8.1 Solve each of the following systems by graphing each of the following. 10. 2x - y = 4 2x - y = 6 12. x-2y = 8 3x - 2y = 12 20. 3x - 6y = 9 X - 2y = 3 26. Find values for m and b in the following system so that the solution

Slope, y intercept

What are the slope, y-intercept, and equation of the line passing through the points (-1,1.2) and (3,-2)? a. slope = -0.8, y-intercept = 0.4, y = -0.8x+0.4 b. slope = 0.8, y-intercept = 0.4, y = 0.8x+0.4 c. slope = -0.8, y-intercept = 1.5, y = -0.8x+1.5 d. slope = -1.25, y-intercept = 0.05, y = -1.25x+0.05

Linear equations

1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function and

Rates and Investments : Systems of Equations Problem

I would like to know if I am on the right track to writin this as a "systems of equations" using the substitution process. How much further do I have to go if this is right so far? A family made an investment for 1 year that earned $7.50 simple interest. If the principal had been $25 more and the interest rate 1% less, the in

Linear systems of quadratic equations and inequalities

Question One The relationship between the load on a reel, L kilonewtons per metre (L kNm 1) and the reel diameter, x metres, is modeled by a graph consisting of two parabolic arcs, AR and BC, as shown. Arc AR is part of the parabola L =px2 + qx +r Points D(0. 1, 2.025), E(0.2, 2.9) and F(0.3, 3.425) lie on arc AR. Setup a syst

A second order system satisfies the differential equation:

A second order system satisfies the attached differential equation: Calculate the natural complete response Xn(t) of the system, provided that: a0 = 13; a1 = 4; x(0) = 1; dx(o)/dt = 4. See attached file for full problem description.

Linear system

Solve the equation. Determine whether it is inconsistent, dependent, or neither. 3x - 2y = 0 9x - 8y = 7

Linear system

Solve the linear system. State whether the system is inconsistent, dependent, or neither. x/6 + y/3 = 8 x/4 + y/2 = 12

System of nonlinear equations

If a system of nonlinear equations contains one equation whose graph is a circle and another equation whose graph is a line, can the system have exactly one solution? If so, what does the graph of the situation look like?

Non-linear system

The following is a non-linear system. Solve it 1/x + 2/y = 3 2/x + 1/y = 4 (Hint: Try a change in variable. Let u = 1/x ; let v = 1/y)

Linear Algebra with Cubic Roots

Exercise. IV. This problem is a partial investigation of which n×n matrices over C have cube roots; that is, for which n × n matrices A over C there is an n × n B over C such that A = B3. Since C is algebraically closed, every n × n matrix over C is similar over C to a matrix in Jordan canonical form. A. Suppose that A

Complex Matrix, Diagonal Matrix, Left and Right Eigenvectors

5. Let X^-1 AX = D, where D is a diagonal matrix. (a) Show that the columns of X are right eigenvectors and the conjugate rows of X^-1 are left eigenvectors of A. (b) Let ... be the eigenvalues of A. Show that there are right eigenvectors x1,. . . , x and left eigenvectors y1, . . , yn such that A =... keywords: matrices

Eigenvalues, eigenfunctions and modified Green's function.

5.6. (a) Find the eigenvalues and eigenfunctions of ?u"=&#955;u, ?1<x<1; u'(1)?u(1) =0, u'(?1)+u(?1) =0 Show that there is precisely one negative eigenvalue, that zero is an eigenvalue, and that there are infinitely many positive eigenvalues. Show graphically how the eigenvalues are determined. (b) Find the modified Green's f

Differential Equations

(See attached file for full problem description) 1) The slope field for the system dx/dt = 2x + 6y dy/dt = 2x - 2y is shown to the right a) determine the type of the equilibrium point at the origin. b) calculate all straight-line solution. 2) show that a matrix of the form A =(a b; -b a) with b!=0 must have complex eig

eigenvalues and eigenvectors of matrix

I have some very basic lin algerbra eigenvalue problems. (See attached file for full problem description) 1. Find the eigenvalues and eigenvectors for the projection matrix P = [0.2 0.4 0; 0.4 0.8 0; 0 0 1]; 2. Find the eigenvalues for the permutation matrix P = [0 1 0; 0 0 1; 1 0 0]; 3. Finish the last row to make the mat

Symplectic Matrix, Eigenvalues and Multiplicity

A 2n x 2n M is symplectic if where J is the (also 2n x 2n) matrix . Prove that if is an eigenvalue of M , then so is , and that these have the same multiplicity. Show furthermore that, if are eigenvalues of M, and , then the corresponding eigenvectors have the property that Please see the attached file for th

Pairwise Sequential Voting

A seventeen-member committee must elect one of four candidates: R, S, T, or W. Their preference schedule as shown below. Which candidate wins under pairwise sequential voting with the predetermined order S, T, W, R? Number of Members Ranking 6 R > S > T > W 5 S > R > T > W 3

Banach Space and Closed Subspace

Let I = [a,b] be a finite interval. Show that the space C(I,R^n) of continuous functions from I into R^n is a Banach space with the uniform norm llull = sup l u(t) l where t is in I. (Show that this is a norm and that C(I,R^n) is complete). See attached file. Please be very detailed when answering question.