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# Linear Algebra

### Linear Algebra - Singular Matrix

Let a,b,c,d,e,f,g,h be reals. Prove that the following matrix A is singular. Matrix A: 0 a 0 0 0 b 0 c 0 0 0 d 0 e 0 0 0 f 0 g 0 0 0 h 0

### Determining system reliability

A system consists of three subsystems in parallel (assume operating redundancy). The individual subsystem reliabilities are as follows: Subsystem A = 0.98 Subsystem B = 0.85 Subsystem C = 0.88 Determine the overall system reliability

### Determining the Probability of a System Surviving: Reliability

A system consists of four subassemblies connected in series. The individuak subassembly reliabilities are as follows: subassembly A=0.98 subassembly B=0.85 subassembly C=0.90 subassembly D=0.88 Determine the overall system reliability

### Systems of Linear Equations - Graphs

Answer the question and solve the problems below. Make sure you show all your work. 1. Determine whether the lines will be perpendicular when graphed. 3x - 2y = 6 2x + 3y = 6 2. Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the num

### Linear Functions #2

Think of a mathematical function that represents something from your own life. For example, suppose the number of beers you drink depends on the number of football games you watch. If you drink five beers during every football game, the function would be: Number of Beers (B) = 5 times Number of Football Games (F), or B = 5F

### Determining the Number of Calculators Produced

The cost C, in dollars, to produce calculators is given by the function C(x)=57x+4500, where x is the number of calculators produced. How many calculators can be produced if the cost is limited to \$61,500?

### Theory Regarding Diagonalization

See attached document.

### MAPE and MAD Linear Regression Model

Senior Management at Esil University believes that decreases in the number of undergraduate applications that they have experienced are directly related to tuition increases. They have collected the following enrollment and tuition fees data for the past decade: Year: Undergraduate Applications: Annual Tuition

### Augmented Matrices and Row Operations

Given the following matrices/vectors: 2 4 1 (-1) 4 a:=0 b:=(-2) A:= 3 1 0 1 6 1 2 1 linear systems: find x,y such that Ax=b and Ay=a (note x, y with vector character over each).

### The Order Axioms

Use the field and order axioms to prove the following proposition: If xy > 0, then either x > 0 and y > 0, or x < 0 and y < 0. Please explain stepwise.

### Linear equations

Please help with the following problem. What are the detailed steps in solving problems such as x+8=30...what steps do you follow? How do you figure what the "X" is ?

### General Theorems That Are Usually Proved in Any Linear Algebra

(a) The row space of a matrix is isomorphic to the column space of its transpose. (b) The row space of a matrix is isomorphic to its column space. Please show and explain work, thank you!

### Matrices, Eigenvalues and Eigenvectors

Let M=[(4 -1 -9 -5), (3 -2 -5 -3), (3 0 -7 -3), (0 -1 1 -1)] i) Show that the column vector [7,5,3,2]^T is an eigenvector for M. ii) Find the eigenvalues for M. iii) Determine whether or not M is diagonalisable over R, justifying your assertion and showing any necessary calculations in full.

### Problems with normal subgroups

Let N_1, ..., N_k be normal subgroups of a finite group G. If G = N_1N_2 ...N_k (the set of all elements of the form a_1a_2...a_k with a_ j in N_ j) and |G| = |N_1| . |N_2| . |N_3| ... |N_k|, prove that G = N_1 x N_2 x N_3 x ... x N_k.

### Approximate the function...vectors, eigenvalues, or taylor series?

Approximate the function x(t)=e^t over the interval (0, 1) using the second order polynomial. From the set of linearly independent function, [1,t,t^2], form an orthonormal set of functions. 1 The inner product is defined as <f(t),g(t)> = â?« f(t)g(t)dt.

### system of linear equations..

Total number of cherries on a plate, in a cup, and in a bowl is 780. The plate contains 145 cherries. The number of cherries in the bowl is 4 times the total number of cherries on the plate and in the cup. How many cherries in the cup?

### Systems and equations

For this SLP I want you to create a system of linear equations from your own life, it can be an extension of your module 2 SLP or something new entirely. Keep in mind that a system of linear equations will consist of two equations using the same variables and the variables will represent the same thing for both equations, i.e.,

### Linear Algebra

P 3 is a vector space of polynomials in x of degree three or less and Dx(p(x)) = the derivative of p(x) is a transformation from P 3 to P 2. a. the nullity of Dx is two. b. The polynomial 2x + 1 is in the kernel of Dx. c. The polynomial 2x + 1 is in the range of Dx. d. The kernel of Dx is all those polynomials in P 3 with

### Linear combination problem

If T: U â?' V is any linear transformation from U to V and B = {u 1, u 2, ..., u n} is a basis for U, then set T(B) = {T(u 1), T(u 2), ... T(u n)} a. spans V b. spans U c. is a basis for V d. is linearly independent e. spans the range of T

### A Simple introduction to eigenvectors and eigenvalues

For the matrix 2 -12 1 -5 We will explain what eigenvalues and eigenvectors are as well as verify given eigenvalues and eigenvectors for this matrix.

### Eigenvalues of the Transition Matrix

A discrete dynamical system model for the population of cheetahs and gazelles in Namibia is given by the following pair of equations: .3Ck + .4 Gk = Ck+1 -pCk + 1.3 Gk = Gk+1 where Ck measures the number of cheetahs present in a certain Namibian game reserve at time K, Gk gives the number of gazelles (measured in tens), a

### substitution or addition/elimination technique

Use substitution or addition/elimination technique to solve system of equations. Show steps of solution. please apply apply both techniques. here it is... 2x + y = 6 x - y = -3

### Linear Algebra: Systems of Equations

Please show all work for the attached questions. 8. A cellular phone company offers a contract for which the cost c, in dollars, of t minutesof telephoning is given by C= 0.259t-300)+79.95, where it is assumed that >300 minutes. What time will keep cost between \$129.95 and \$167.20? - For the cost

### need help w/algabra Axia College MAT 117 appendix d

1. The cost, in millions of dollars, to remove x % of pollution in a lake modeled by C = 6000 / (200 - 2x) a. What is the cost to remove 75% of the pollutant? b. What is the cost to remove 90% of the pollutant? c. What is the cost to remove 99% of the pollutant? d. For what value is this equation undefined? e. D

### Computer graphics and linear algebra

Why is linear algebra important for computer graphics? How are linear algebra techniques used in computer graphics? Please review the following link,Mathematics for Computer Graphics, Retrieved February 29, 2008, from http://www.cc.gatech.edu/~turk/math_gr.htmlVectors and Matrices, Retrieved February 29, 2008, from http:/

### Relevance of Mathematical Modeling of Sociological Phenomenon

We will be looking at a common application of linear algebra in sociology and psychology, the domination matrix. Click on the links below and read through the descriptions of these applications: Domination Matrix, Retrieved February 29, 2008, from http://media.pearsoncmg.com/aw/aw_lay_linearalg_3/cs_apps/dominance.pdf Gra

### Determining if a System as Stable or Unstable

Please show steps to evaluate for correct answer. 1. Systems are unstable if their characteristic equations have a positive root (solution). Determine whether each of the following characteristic equations represents a stable or unstable system. (i) s^3 + 6 s^2 + 11 s + 6 = 0 (ii) s^3 + s^2 - 8 s - 12 = 0 2) In a Hook

### Goldbach's conjecture

One of the most famous unsolved problems in mathematics is a conjecture made by Christian Goldbach in a letter to Leonhard Euler in 1742. The conjecture made in this letter is now known as Goldbach's Conjecture. The conjecture is as follows: Every even integer greater than 2 can be expressed as the sum of two (not necessarily

### Eigenvalues and Transformations

Please show the complete steps. 1. Let T: P2 -> P1 be the linear transformation defined by T(p(x)) = p'(x) + p(x). Show that T is linear. 2. Find the matrix for the transformation T given in problem 1 with respect to the standard basis {1, x, x^2}. Then, find all eigenvalues and corresponding eigenvectors for T. 3. True

### Prove that limit_(x->c) h(x) does not exist.

Let f: D -> R and g: D->R where D is an open interval that contains the point c and let f and g be functions that are defined on D except possibly at point c. Suppose that limit_(x->c) f(x) exists and that limit_(x->c) g(x) does not exist. Define the function h(x) = f(x) + g(x). Prove that limit_(x->c) h(x) does not exi