### Bounded Linear Operators and Bounded Invertibles

Please solve the attached problems on bounded linear operators and bounded invertible equations.

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Please solve the attached problems on bounded linear operators and bounded invertible equations.

Solve for x(1), x(2), x(3); 1. 27,954.606 x(1) + 11,969.843 x(2) - 7515.1688 x(3) = 6124.3394 2. 11,969.843 x(1) + 5900.332 x(2) - 3586.4121 x(3) = 3054.3092 3. -7515.1688 x(1) - 3586.4121 x(2) + 2513.4532 x(3) = -1756.4525

A-Solve: 4x=3y-6 4y=3x+1 b-Solve: 3x+4y=8 y=-3x+2

Let p be a prime in Z. Define Z(p) = {m/n in rational Q | p does not divide n} i) Show that Z(p) is a subdomain of Q ii) Find the units in Z(p) ,

1) Let { 1, 2, 2........... n} be a basis of an n dimensional vector space over R and A be n Matrix . Let ( 1, 2, 3............... s) = ( 1, 2, 2........... n) A Prove that dim (span { 1, 2, 3............... s}) = Rank (A). 2) Let V1 be the solution space of x1 +x2 + x3............+xn = 0 let V2 be the solution spac

.....is a commutative diagram of groups and that the rows are exact,... being homomorphisms. Prove that (a) if and are surjections and is an injection, then is an injection. (b) if , and are injections, then is an injection. 2. For a group extension {e} B H G {e} Prove that G ~ H/ (B).

See attachment for question. 1 Suppose that  is a finite dimensional normed linear space. a) Let be a basis for . Define Prove that 1, the closed unit ball in , is compact in (, ) b) Prove that any two norms on  are equivalent.

Suppose that N is a normed linear space. Prove that each finite dimensional linear submanifold of N is complete and therefore closed.

1. Let G be a group and H be a subgroup of G of index equal to 2. Prove that H G 2. Let (G,?) be a group and H G. Prove that if G/H is a p-group and is a p-group then is a p-group H. Please see the attached file for the fully formatted problems.

Given a 3x3 matrix M whose individual rows add up to 1 find a 3x1 vector v (not all zero) such that v=Mv. (Hint: Do a few examples.)

An event F is said to carry negative information about an event E, and we write.... Prove or give counterexamples to the following assertions... (See attachment for full question)

A, B and C are matrices. What are their ranks? A) 1 2 3 4 5 6 B) 1 1 1 1 C) 3 3 7 7 11 11

10. A psychology laboratory conducting dream research contains 3 rooms, with 2 beds in each room. If 3 sets of identical twins are to be assigned to these 6 beds so that each set of twins sleeps in different beds in the same room, how many assignments are possible?

1. Many free software mathematics packages on the Internet will solve a system of equations given the coefficients in the system. Problem: find out which of the four techniques (the Method of Addition, the Method of Substitution, Gauss-Jordan Elimination, and Cramer's Rule) is used in the majority of these types of software p

Please see the attached files for the fully formatted problems. This question is concerned with finding the solution of the first order simultaneous equations where a = -2, b = 8, c = -24, d = 30 (i) Find the particular solutions to the differential equations which satisfy the initial conditions x = 16 and y = 3 at t

1) An augmented matrix of a linear system has been reduced by row operations to the following form. Continue the appropriate row operations and describe the solution set of the original system. Please show every step no matter how minor, use the brackets for each reduction and write out every equation change. Please leave

8. Let R be a relation on a set S such that R is symmetric and transitive and for each x ε S there is an element y ε S such that x R y. Prove that R is an equivalence relation (i.e. prove that R is reflexive)

51. Solve the system: x^2 + xy^3 = 9 3x^2y - y^3 = 4 using Newton's method for nonlinear system. Use each of the initial guesses: (x_0, y_0) = (1.2, 2.5), (-2, 2.5), (-1.2, -2.5), (2, -2.5) Observe which root to which the method converges, the number or iterates required, and the speed of convergence.

The reduced row-echelon forms of the augmented matrices of three systems are given in the attachment. How many solutions does each system have? 1. The reduced row-echelon forms of the augmented matrices of three systems are given below. How many solutions does each system have? a. │1 0 2 0│ 	

27. Emile and Gertrude are brother and sister. Emile has twice as many sisters as brothers, and Gertrude has just as many brothers as sisters. How many children are there in this family? Please see attachment for the rest of the questions.

1.Simplify -i^4: answers a.-1 b.1 c.i d.-i 2.Types of Equations Solve by factoring: x4 - 9x2 = 0. answers a.1, -1, 3, -3 b.0, 3, -3 c.9, -9 d.3, -3 3. Two-Dimensional Coordinate System and Graphs; Find the midpoint of the line segment with endpoints (-4, 8) and (7, 2). a.(3/2, 5) b(-11/2, 3) c.(11/2, -3)

Can you help me answer question by explaining each step please? Find the eigenvectors and eigenvalues of the matrix A = ( 1 3 0 1 1 1 0 1 1 ) Check that all the eigenvectors, v, and the corresponding eigenvalues, are correct by showing that they satisfy Av=Yv

Real Analysis Gradient, Divergence and Curl (II) Verify 1.▼*(F × G) =G*&

1. Solve the inequality. Write the solution in interval notation and graph the set on the number line. -2(x - 4) 3x + 1 - 5x 2. Solve the following problem by writing an equation and then solving the equation: You invest $7,200 in two accounts paying 8% and 10% annual interest respectively. At the end of the year, the acco

How does the region of overlap on a graph determine the solution of a system of linear inequalities?

See page four, the question is question # 2. Show that P^2= P^T = P and that C(P) = C(A)

Let A be the real 2x2 matrix [a b] [c d] with bc greater than or equal to 0. Prove there exists a real 2x2 invertible matrix S so that S^-1 A S is either diagonal or of the form [x 1] [0 x] where x is the eigenvalue of A.

Let B be an nxn matrix with B^2 = B prove that B is diagonalizable, ie there exists an invertible matrix S so that S^-1 B S is diagonal. (Hint: all eigenvalues of B are either 0 or 1. For each k between 0 and n, consider the case when the nullity of B is k.)

1) If a Matrix A is diagonizable, must it have an inverse ? if so, is it diagonizable? Can {see attachment} be diagonized, does it have an inverse as well as {see attachment} 2) A is mxn For m<n, is there a vector b such that Ax = b does not have any solution? Any trivial solution for Ax = 0? b) Can say the same for m>n ? A