Can a closed linear map be unbounded?

Expert Solution

I gave proof also if u need.

Colby Messinger answered 1 year ago

Is the interval [-4, 7) open, closed, half–open, or unbounded?

1. Explain how a linear program with an unbounded feasible region may have a maximum solution....

1. Explain how a linear program with an unbounded feasible region may have a maximum solution. Explain how a linear program with an unbounded feasible region may have a minimum solution. If you find it difficult to write an explanation, you may draw graphical examples to illustrate your point. 2.If a linear program with two input variables (a two-dimensional problem) has N constraints and has a non-trivial bounded feasible region then what is the maximum number of sides to the...

Let L be a linear map between linear spaces U and V, such that L: U...

Let L be a linear map between linear spaces U and V, such that L: U -> V and let l_{ij} be the matrix associated with L w.r.t bases {u_i} and {v_i}. Show l_{ij} changes w.r.t a change of bases (i.e u_i -> u'_i and v_j -> v'_j)

Determine whether the following linear optimization problem is infeasible, unbounded, or has multiple optimal solutions. Draw...

Determine whether the following linear optimization problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion. Maximize 20x + 50y Subject to -3x + 4y < 120 2x + 3y > 180 x, y > 0

Determine whether the following linear optimization problem is infeasible, unbounded, or has multiple optimal solutions. Draw...

Determine whether the following linear optimization problem is infeasible, unbounded, or has multiple optimal solutions. Draw a graph and explain your conclusion. Maximize 20x + 50y Subject to -3x + 4y < 120 2x + 3y > 180 x, y > 0

Find the kernel (or nullspace) and the image of each linear map together with their basis....

Find the kernel (or nullspace) and the image of each linear map together with their basis. (a) T :R4 →R3 given by f(x,y,z,w)=(3x+y−3z+3w , x+y+z+w , 2x+y−z+2w) (b) T :R3 →R5 given by f(x,y,z)=(2x−y+6z , x−y−z , x+y−5z , z−y , −x+2z) c) T :R4 →R3 given by f(x,y,z,w)=(x−y−3z+w , 2x−3y+z+2w , 3x+y−4z−w)

suppose that T : V → V is a linear map on a finite-dimensional vector space...

suppose that T : V → V is a linear map on a finite-dimensional vector space V such that dim range T = dim range T2. Show that V = range T ⊕null T. (Hint: Show that null T = null T2, null T ∩ range T = {0}, and apply the fundamental theorem of linear maps.)

Let A be a bounded linear operator on Hilbert space. Show that if R(A) is closed,...

Let A be a bounded linear operator on Hilbert space. Show that if R(A) is closed, so is R(A*)

(3) Consider the linear map ? : R2 → R2 which sends (1, 0) ↦→ (−3,...

(3) Consider the linear map ? : R2 → R2 which sends (1, 0) ↦→ (−3, 5) and (0, 1) ↦→ (4, −1). (a) What is the matrix of the transformation? What is the change of coordinates matrix? Do they agree? How come? (b) Where does this transformation send the area between the vector (4, 2) and the x-axis? Explain algebraically and draw a picture. (c) What is the image of the lower half plane under ?? Explain algebraically and...

Question 2. True or false 2. If [T]β is the matrix representing the linear map T...

Question 2. True or false 2. If [T]β is the matrix representing the linear map T in the basis β, then the jth column of [T]β contain the coordinates of the T(βj) in the basis β, and same for the rows.

Question

Can a closed linear map be unbounded?

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Is the interval [-4, 7) open, closed, half–open, or unbounded?

1. Explain how a linear program with an unbounded feasible region may have a maximum solution....

Let L be a linear map between linear spaces U and V, such that L: U...

Determine whether the following linear optimization problem is infeasible, unbounded, or has multiple optimal solutions. Draw...

Determine whether the following linear optimization problem is infeasible, unbounded, or has multiple optimal solutions. Draw...

Find the kernel (or nullspace) and the image of each linear map together with their basis....

suppose that T : V → V is a linear map on a finite-dimensional vector space...

Let A be a bounded linear operator on Hilbert space. Show that if R(A) is closed,...

(3) Consider the linear map ? : R2 → R2 which sends (1, 0) ↦→ (−3,...

Question 2. True or false 2. If [T]β is the matrix representing the linear map T...