Let L: R→ R be a linear operator such that L X2 )= X3-X2, then L Select one: O a. b. O d.

Q: Let T be the linear operator on R defined by T(x,,x, x) = (2x1, x, - x, 5x, + 4x, + x,). Then 7 is…

A: First express the linear operator in matrix form and then use the matrix to calculate the inverse…

Q: Consider the following linear operator; T : R → R° given by T(x, y, z) = (y, x + z, z).

A: We have to find the real Eigen value of T

Q: . Show that the operators T₁,, T4 from R2 into R2 defined by (1, 2) (1, 0) (§1, §2) (0, §₂) (§1, §2)…

A:

Q: Let X be a normed linear space and T: X→ X and S: X → X be two bounded linear operators, then SoT…

A:

Q: 3. Let L be a linear operator on R and let L(1) = a . Show that L(x) = ax for all x E R .

A:

Q: Accept that (C'[0, 1], || - ||1) is a Banach space, where c'(0, 1] := {x € C[0, 1] : a'(t) E C[0,…

A: Consider the given C10,1:x∈C0,1:x'(t)∈C0,1 and x1=supt∈[0,1]x(t)+supt∈[0,1]x'(t)ddt=1

Q: Show that the operators T and T₂ from 2 R² into R² de fined by T₁: (F₁) √₂ ) → (9₂9₁) and T2=…

A:

Q: Let L:R R be a linear operator such that L X2 = X1 then Ker(L) spanned by: -> Select one: a. (e2,e3)…

A:

Q: Find a norm of the operator A(x) = o (s4 + s? )x(t)dt in space C[0, 1]. a. 4 Ob. O c. 2 4 O d. 15 1…

A:

Q: Let LR→ R be a linear operator such that L X, )=| x, then Im(L) spanned by: Select one: a. (0,e,,e2)…

A:

Q: Let L:R R be a linear operator such that L X2 X3- X2 then Ker(L) spanned by: Select one: (e, e )

A:

Q: Let L:R → R3 be a linear operator such that L( X2 X1 then Im(L) spanned by: X3 X1 Select one: a. O…

A:

Q: Show that the operators Ix=x 0x = 0 Tx (t)=n't & are Linear. 6

A:

Q: (6) Suppose that T is a linear operator on a 2 dimensional vector space V and that T+ a I for any a…

A:

Q: Let X be a Banach space and TE B(X) an operator with ||T|| E o(T). Show that || id +T|| = 1+ ||T||.

A:

Q: Consider the D-operator P(D) = mD² + 2kD +¢, where m and c are positive. If -c/m < k< 0, then

A:

Q: If S and T are normal linear operators satisfying ST* = T* S and TS* = S*T, show that their sum S+T…

A: I have used just definition of normal operator

Q: Let T: X→→→→→ Y be a linear operator and dim X = dim Y=n<∞. Show that R(T) = Y if and only if T¹…

A:

Q: Let A: C [0,1]→C [0,1]. Prove that operator A is continuous reversible, find A!, 2.11. Ax(1) = x(1)…

A: We have given operator A such that A: C[0,1]-C[0,1].Also we must know that the inverse operator…

Q: Let A€BL(H) be a compact operator, then show that A*A is a compact

A:

Q: 3. Let T: R³ R³ be the operator given by 00 8 1 0 T(v) = -12 6 υ. Determine whether T is…

A:

Q: Let L: R2 → R2² be the linear operator defined by L 2

A:

Q: Let T: R-R° be a linear operator given by T(x, y, z) = (x+y, x-y, 0) which of the following vector…

A: You have attached question 8 only but above thta you mention Q7.I am answering question 8.

Q: Show that the operators T,··, T4 from R² into R² defined by ... (§i, 52)→ (Š1,0) (§1, É2)→ (0, E2)…

A:

Q: 2. Let T: R³ → R³ be the operator given by -1 1 0 -1 0 0 Determine whether T is decomposable or…

A:

Q: 2. Let T: R³ R³ be the operator given by 1 1 T(v) = 9). 1 Determine whether T is decomposable or…

A: Consider the given operator, Tv=-1100-1100-1v Here we need to determine that whether T is…

Q: a bonneled linear operator. Then prve. that. Kes's is clased. b) let 8:X>y be a

A:

Q: Let L:R3 → R3 be a linear operator, if L(X) = L(Y), then X= Y. Select one: True O False

A: Explanation:

Q: If T: V → V is a linear operator with minimal polynomial х — 2, then T is diagonalizable. True False

A:

Q: .

A: Given: L is the linear operator on and it is define by,

Q: et L:RR be a linear operator such that L x2 )-X1, then Im(L) spanned by= X3 X1 Gelect one: a. O b.…

A: T : A  → B thenIm(T) = { TX : X ∈ A}

Q: Question 5. Let T : V → V be a linear operator satisfying T² = T. Define U1 = {v € V : T(v) U2 = {v…

A: Given: U1=v∈V:Tv=v U2=v∈V:Tv=0 T2=T Objective: To show that V=U1⊕U2 That means to show that every…

Q: Let L:R R be a linear operator such that L X2 X 1 then Im(L) spanned by: Select one: a. Ob. (0,e.e)…

A:

Q: Let L: R→ R be a linear operator such that L X2 )= X3-X2, then Ker(L) spanned by: X3 X3-X1. Select…

A:

Q: Let T be function from R to R2 de fined T (x) = (x, x), Then T is linear operator True O False O

A:

Q: 2. Let T : R³ → R³ be the operator given by -1 1 0 0 −1 1 0 0 – 1 - T(v) = = v. Determine whether T…

A: given matrix T=-1100-1100-1 determine whether it is decomposable or indecomposable.

Q: Let L: R → R be a linear operator such that L X2 )=| X1 then Ker(L) spanned by: Select one: а. b.…

A: Given a linear operator L from R3 to R3. We need to find the set of vectors that spans Ker(L)

Q: Consider the following operator A : L²[0, 1] → L'[0, 1] A(f)(x) = (f(x))² + f(x). If this a linear…

A: Given, the operator  A : L20, 1→L10, 1 defind by                               A(f)(x)=(f(x))2+f(x)…

Q: 4) Let V be the vector space of polynomials of degree < 2 and let p(x) = ax² + bx + c. Find the…

A: Given that, The definition for adjoint linear operator is, Let V and U be two vector space over the…

Q: If V = W1 e ... Wk, then there exist k linear operators E,, .., E, On V such (1) each E, is a…

A:

Q: Let T:R→R² be a linear operator defined by T(x,y)= (w,w,) where w, =x –-y and W, =-2r- y. %3D %3D…

A: T0Tx = T(t(x))

Q: Consider the spaces lP = P(N), 1 <p<00, i=0 For which pairs of (p, q), is the identity map I : x → x…

A:

Q: Let g C[0, 1] be a fixed function. Consider the operator A = B(C[0, 1]) defined by (Au) (s) :=…

A: Compact Operator: A compact operator is a linear operator A:X→Y where X, Y are normed vector spaces…

Q: Conversely, if T :V V is a linear operator such that T2 = T, show that V = kerT O imT. [Hint: 3.b, v…

A:

Q: Let L: R → R° be a linear operator such that L X2 X3- X2 X3- X1 then L 0 )= X3 Select one: а. 1 b.…

A:

Q: Find a norm of the operator A(x) = (t³ + 2t2)x(t) in space C[0, 1]. O a. 3 O b. 4 7 2 3 O d. 6 O e.…

A:

Q: Let L:R3 → R3 be a linear operator, if L(X)= L(Y), then X Y. Select one: O True False

A:

Q: Let L:R→ R be a linear operator such that L X2 )=x1, then Im(L) spanned by: -> X3 Select one: a. 一 O…

A: The given linear operator is: L:ℝ3→ℝ3 such that Lx1x2x3=x1x1x1

Q: Determine whether the following are linear operatorson Rn×n. L (A) = A − AT

A:

Q: Suppose L: R → R° be defined by u, +17 Lu2 2u2 %3D Uz Uz Determine whether L is a linear operator or…

A: According to question given :L:R3→R3Lu1u2u3=u1+12u2u3We have to determine whether L is a linear…