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Using the method of undetermined coefficients, find the solution of the system:
Let u = x + y/ 1-xy and v = tan-1x + tan-1y . If xy?1 , show that u and v are functionally related and find the relationship.
Fundamental subspace theorem.Show that the fundamental subspace theorem holds
Work distribution and equation solving. Solve using the Gaussian Elimination and show all work.
Suppose that {an} and {bn} are sequences of positive terms, and that the limit as n goes to infinity of (an/bn) = L > 0.
Use the inequality from part (b) to show that sn 0. Conclude the sequence is increasing.
A company produces desks on both the east and west coast. The east coast plant, fixed costs are 16000 per year and the cost of producing each desk is $90.
Matrices : Vector Equations.Step by step instructions and name each step like triangular form
Let r satisfy r2=r+1. Show that the sequence sn=Arn, where A is any constant, satisfies the Fibonacci relationship.
How many multiplications are necessary to find the determinants of matrices which are 2x2, 3x3, 4x4?
Find all solutions of the equations using Gauss-Jordan elimination.
If lim n-->infinity (a_n*b_n) exists and lim n--> infinity (a_n) exists, then lim n -->infinity (b_n) exists.
Use the chain rule to find dw / dt, where w = x^2 + y^2 + z^2, x=(e^t) cos t, y=(e^t) sin t, z=(e^t), t=0.
Systems of Equations : Real World Situations and Solving Determinants
Gaussian Elimination and Back Substitution
Suppose An is the n by n tridiagonal matrix with 1's everywhere on the three diagonals:
Assuming that 10 observations are adequate for these purposes, determine the 3-sigma control limits for defects per shirt?
Discuss also the continuity of each of the following functions at given point c. Give reasons to your answers.
Please explain in your own words the duality principle.The biggest problem I have with matrices is the multiplication.
Given a =2i +3j, b = 3i +5j , and c = 8i + 11j express c in the form ra+ sb where r and s are scalars.
Given that 1-x+x^2+...+(-x)^n is a power series representation for 1/(1+x), find a power series representation for (x^3)/(1+x^2).
Parametric equations and matrices.The diagram below shows a line defined by the parametric equations
When you first begin to draw the graph of f(x), why do you start where you do? How high do I go when drawing a graph? How do I know when to stop?
Problem on Limits and Continuity. Provide complete and step by step solution for the question and show calculations and use formulas.
Invertibility of Matrices.Explain why the columns of the nxn matrix A span R^n when A is invertible?