Solving Linear Systems of Equations with 3 Variables
Solve the linear system. Indiciate if the system is inconsistent, dependent, or neither. 3x + 2y + z = 2 4x - y + 3z = -16 x + 3y - z = 12 keywords: 3, x, y, z
Solve the linear system. Indiciate if the system is inconsistent, dependent, or neither. 3x + 2y + z = 2 4x - y + 3z = -16 x + 3y - z = 12 keywords: 3, x, y, z
Solve the equation. Determine whether it is inconsistent, dependent, or neither. 3x - 2y = 0 9x - 8y = 7
Solve the linear system. State whether the system is inconsistent, dependent, or neither. x/6 + y/3 = 8 x/4 + y/2 = 12
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?
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)
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
Three functions e^x, sinx and cosx are given. They must be shown linear independent by using Wronskian.
I have another question on linear approximation using e. Suppose I want to approximate e^ 0.9. I am assuming that I let f(x) equal the following e^ 0.9 ~ e^0.5 + e^0.5 (0.9-0.5) = 0.4e^0.5 Am I on the right track?
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
Find four elements of the field that form a subfield of order 4.
5.6. (a) Find the eigenvalues and eigenfunctions of ?u"=λu, ?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
(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
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
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
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
Get a 3x3 matrix equation with solution [A B C]T provides a least squares fit of the n data points: (t1, b1),...,(tn,bn) to the curve of form f(t) = A + Bsin(t) + Ccos(t)
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.
Combine from JPE, Fall 90 and Spring 97) Let A ∈ C^(n X n) be a normal matrix. a. Prove that A - M is normal for any λ ∈ C. Prove that ||Ax||2 - ||∧*x||2 for all x ∈ C^n b. Prove that ( λ, x) is an eigenpair of A if (λ, x) is an eigenpair of A*. (Hence A and A* have the same eigenvectors.
See the attachments. Let F be a field and . Then is an n - dimensional vector space over F. Define a function by . (a) Show that T is a linear operator. (b) Find the characteristic and minimal polynomials for T, with explanation. (For the characteristic polynomial, recall that you will need to choose a basis for
Suppose that V is an inner-product space. Prove that if T: V-->V is a positive operator and trace(T)=0, then T=0.
Let X be any vector space over the field F, let L be a linearly independent subset of X, and A be the set of linearly independent subsets of X containing L. Then A is partially ordered by inclusion - why does it follow?
A) Solve the equation uxy = x^2 y and its particular solution fur which u(1,y)= cos(y). b) Determine whether each of the following partial differential equations is linear or nonlinear, state the order of the equation, and name the dependent and independent variables. i) ut=9uyy ii) x^2Pzz = z^2Pxx iii) WWrr=pqr iv) sxx + s
Let T be a closed linear operator with domain D(T) in a Banach space X and range R(T) in a normed space Y. If T^-1 exists and is bounded, show that R(T) is closed.
If the inverse T^-1 of a closed linear operator T exists, show that T^-1 is a closed linear operator.
1. When an input x(n) = is applied to a digital filter (which is a linear system), the output is . (a) Find the transfer function of the system, (b) Find the response of the system to a sinusoidal input, Please see the attached file for the fully formatted problems.
2. The time-dependent variables z, y and z satisfy the system of equations Xdot = AX where (a) Show that the characteristic equation for the matrix A may be written as .... (b) In the case of A = 3 determine the corresponding eigenvector. (c) Given that the eigenvectors corresponding to the eigenvalues .. and ... are res
I need the proof of the Linear programming problem attached. --- Consider the LP: Min ct x Subject to Ax ≥ b, x ≥ 0. One can convert the problem to an equivalent one with equality constraints by using slack variables. Suppose that the optimal basis for the equality constrained problem is B. Prove t
Please prove the properties of condition numbers attached to this message. Refer to definitions/theorems you used. Also, if you want, have a look at the second file attached, since I believe that you can refer to the previous properties to do 6 to 10. 7. For any orthogonal matrix Q, i2(QA) = k2(AQ) = k2(A) 8. If D= diag(d1,
Find the cofactor of each element of A=[-1 1 2 3; 1 2 3 4; -1 1 -1 5; 1 -1 1 2] and also the inverse. I am having trouble with this 4 x 4 matrix.
Please see the attached file for the fully formatted problems.