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.
Find the row echelon form (not the reduced row echelon form) of the 4 X 3 matrix whose rows are as follows: row 1: 1/3 1/4 1/5 row 2: 2/3 2/4 2/5 row 3: 3/3 3/4 3/5 row 4: 4/3 4/4 4/5
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
(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.
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.
Let @:G-->H be a homomorphism of G onto H, and let N be a normal subgroup of G. Show that @(N) is a normal subgroup of H. How do I prove that a mapping is a normal subgroup of a group? What I am missing here is some understanding of the terminology and some clear understanding of mappings, homomorphisms, subgroups and no
Find the Eigen Values ( or Characteristic roots ) and Eigen Vectors ( or Characteristic vectors ) of the following matrix and give the Matrix which transforms A to diagonal form. -2 1 1 A = -11 4 5 -1 1 0 To see the question in its correct form, please download the attached que
Question (1): Let T: R^3 into R^3 be a linear transformation defined by T(x, y, z) = (x + 2y - z, y + z, x + y - 2z ) Find a basis and the dimension of ( i ) Range of T ( ii) the Kernel of T Question (2) : If T:R^4 into R^3 is a linear transformation defined by T( a, b, c, d) = ( a - b + c + d, a + 2c - d,
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.
I need to solve the in equality: 2x + 8 <= -16 + 8x For the equation 4x - 2y = 6 find the (a) slope 4/2 (b) y - intercept. (0, -3) Solve the system by the method of your choice 2x + 3y = 5 3x + 2y = -5
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)
See the attached file. 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
Problems 4.2 1, 2, 5, 16, 17, 19, 23, 24, 25, 30, 31, 32, 35 and 36. (page 159 - ) See attached file for full problem description.
Problems 4.1 1, 2, 3, 6, 7, 8, 9, 11, 15 and 16. (page 147) I attached few pages description. See attached file for full problem description.
Question (1) Find a basis and dimension of the subspace W of R4 generated by the vectors ( 1 , - 4 , - 2 , 1 ) , ( 1 , - 3 , - 1 , 2 ) , ( 3 , - 8 , - 2 , 7 ) . Extend it to find the basis of R4 Question (2) Determine a basis and the dimensions of the Subspace of M2(R) generated by the 2 by 2 Matrices [ 2 -10 ] , [
Question (1) Find a basis and dimension of the subspace W of R4 generated by the vectors ( 1 , - 4 , - 2 , 1 ) , ( 1 , - 3 , - 1 , 2 ) , ( 3 , - 8 , - 2 , 7 ) . Extend it to find the basis of R4 . Question (2) Determine a basis and the dimensions of the Subspace of M2(R) generated by the 2 by 2 Matrices [ 2 -10 ] , [
Question : Prove that ( 1 , 3 , 2 ) , ( 1 , - 7 , - 8 ) , ( 2 , 1 , - 1 ) of V3( R) is linearly independent.
Suppose G is a finite group with the property that every non-identity element has prime order (D3 and D5 are examples of groups with this property). Show that if the center of G, Z(G), is not trivial, then every nonidentity element of G has the same order.
Find the general solution (determine eigenvalues) of the system x'(t) = Ax(t) See attached file for full problem description.
Solve the system of equations using the addition (elimination) method. If the answer is a unique solution, present it as an ordered pair (x, y). If not, specify whether the answer is "no solution" or "infinitely many solutions". 3x - 2y = 7 -9x + 6y = -21
Whenever a formula is used, begin by typing the formula you intend to use. Make sure to subscript where appropriate. Solve the system of equations using the substitution method. If the answer is a unique solution, present it as an ordered pair (x, y). If not, specify whether the answer is "no solution" or "infinitely many soluti
-4x + 3y = 9 -12x - 7y = -4
From The Elements of Integration and Lebesgue Measure written by R.G. Bartle 6.T. and 6.U. (attached) See attached file for full problem description.
Please help with these problems. See attached file for full problem description. 1. Find 2. a) Find the inverse of: . b) Use it to solve the following system of equations: 2x1 + x2 + x3 = 4 x2 + 2x3 = 0 2x1 + 2x2 + x3 = 1.
The three elementary row operations come from a very natural place - they are the matrix equivalent of the same three operations allowed when reducing and solving a system of equations. See attached file for full problem description. Clearly explain, matrix by matrix, how the row operations correspond to operations on t
5. In general, a matrix's row echelon form can vary a bit. A matrix's reduced row echelon form is always unique. In other words, there is only one specific reduced row echelon form matrix associated with each matrix. (a) Consider the following homogeneous system: 2x1 ¡ x2 + x4 + 4x5 = 0 2x1 ¡ 2x2 + x3 + 4x4 ¡ 3x5 = 0 2x
A company 403(b) plan allows employees to divide their investments among three mutual funds: an aggressive growth fund, a hybrid fund, and an income fund. The aggressive growth fund currently owns 90% stocks, 5% bonds, and 5% cash. The hybrid fund owns 60% stocks, 20% bonds, and 20% cash. The income fund owns 25% stocks, 50%
(a) Show that if ad = bc ≠ 0 then the reduced row echelon form of [a b] is [1 0] [c d] [0 1] Assume that a ≠ 0. (b) Use your answer to part (a) to show that the linear system ax + by = k cx + dy = l has exactly one solution when ad - bc ≠ 0. (c) If ad - bc = 0, under what conditions will the system
2. A computer manufacturer produces three models of hardware: a desktop, a laptop, and a server. The production times for the desktop are 0.5 hours of assembly and 0.1 of packag- ing. For the laptop, it takes 1.0 hours of assembly and 0.6 hours of packaging. The server requires 1.5 hours of assembly and 1.2 hours of packaging
8.1 Exercises Solve each of the following systems by graphing. 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 to the system is (-3, 4). 5x + 7y = b Mx + y = 22 8.2 Exerc