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    Linear Algebra

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    Solving Homogenous Systems of Linear Equations

    See the attached file. 1. Solve to the homogenous system of linear equations. {2x - 2y + z = 0 both equations are in the same { {-2x + y + z = 0 I got the following: x = ¾c, y = -c, z = 1/2c 2. Find the real solutions to the system of equations using the addition method. x^2 + 8y^2 = 5 x^2 - 4y

    Systems of Equations and Word Problems

    Please see the attached file for the fully formatted problems. 1. A total of $25,000 is invested in two funds paying 8% and 14% simple interest. The total yearly interest is $29,000. How much of the $25,000 is invested at each rate? 2. Solve the system by elimination 3x - y = 17 5x+5y = -5 3x + 2y = 10 2x+5y = 3

    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 Transformations - Unique Solutions

    Show that the system of equations 2x + y + z = -6a 2x + y + (b +1)z = 4 bx + 3y + 2z = 2a Has a unique solution except when b = 0 and b = 6. If b = 0, show that there is only one value for a for which a solution exists, and find the general solution in this case. Discuss the case when b = 6. Interpret your so

    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

    Use linear systems to solve problems

    (See attached file for full problem description) I am looking for a response similar to the BrainMass example mathematics response, which clearly explained how the answer was found.

    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.