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

Q: Let T be function from R to R defined as T (z) = (r, x), %3D Then T is not linear operator O True…

A: FALSE  the detailed explanation is as follows below:

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: 7. Prove that 0* the identity. O and i = i where 0 is the zero linear operator and i is

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Q: Let f = 12r + kry + Jryz re-express f O f(r,y,z) = (x, ry, Tyz+) O {r,y) = (x, ry, ryz*) O f(x,y) =…

A: GIVEN f= ix+kxy+jxyz4     ....(1)

Q: Linear operator T: R2 R2 is defined by T(1,0) (1,4), T(1,1)-(2,2) T one-to-one?

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Q: Jse the Wronskian to prove that the given functions are linearly independent on the real ne…

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

A: Given Linear operator is  L:R3→R3 we have to check if L(X)=L(Y) the X=Y

Q: Vx E X, (x, x) ¢ R. X = {1,2,3}, h of the following relations R on X is irreflexive?

A: Here given set   X={1,2,3}   we know that relation is irreflexive when each x belong X (x,x) dose…

Q: Let 0 <a < b. There exists a c such that a <c<b and + t³ dt = V1+ b- a o V1+63 – V1+a³ - b-a | o…

A: Mean value theorem

Q: Let S and T be linear operators on V and assume that ST =TS (function composition). (a) Show that…

A: ANSWER :

Q: 9 T1, T2 are normal operators on an laner produce space with the property that either commutes with…

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Q: Let L: R → R³ be a linear operator such that X 1 1 L X2 X3 - X2 , then L 0 1 X3 X3 - X1 Select one:…

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Q: b) A function g: Z → Zis defined by the rule g(m, n) = m + n Determine whether it is onto or not..

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: 3. Let f: A-→ B and g : B A be functions. Suppose that y = f (x) if and only if r =g (y). Prove that…

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Q: Prove that f-(U B: -U(B.), %3D i=1 i=1 and n N (B.). 3=D1 i=1

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

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Q: Let T: R² R2 be a linear operator defined by Find a formula for T I Y T[H]-[2] + [2] = [3]. 5

A: To find the formula for the linear transformation of [x y].

Q: The Hamacher product is the t-norm given by ab t(a,b) = a +b – ab Show that this function satisfies…

A: Here the Hamacher product is the t-norm given by t(a,b)=aba+b-ab We have to show that this function…

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

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

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Q: each linear operator T on V, find the minimal polynomial of T. (d) V = Mnxn(R) and T(A)=At . Hint:…

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Q: Ques. 3: Check whether the operator T: R2 → R² defined by T(x,y) = (y,x) is linear. Moreover if T is…

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

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Q: HE- [X2-X1] X3 - X2 , then Ker(L) spanned by: Let L:R3 → R3 be a linear operator such that L X2 %3D…

A: Solution of question as follows

Q: Let L:R3 → R3 be a linear operator such that L ×2 X3 - X2 , then Ker(L) spanned by: X3- X1. X3…

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

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Q: → Det f : V → Il Xa be defined as : a e A f (v) = (fa(v)) a e A where fa : V ¸Xa for each a e A. Let…

A:

Q: Let T be the linear functional defined on C [a b] (with sup norm) by T (x) = ex (t) dt for x eC[a,…

A: Since T is a linear functional defined on        C [a,b]

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

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

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Q: A E R"X", Q e R"Xn and Q > 0, C e R™×n. For a given X € R"Xn and X > 0, define the operator h as…

A: For a square matrix, the trace is the sum of the diagonal entries. Since diagonal can be obtained…

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)…

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

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

A: Solution of question as follows

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 T: X X be the linear operator defined as K = 4. if N is even, K = , if N is odd, %3D Tx(t) = a2)…

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Q: Let X and Y be t function discrete ran X--1 1, 2. y-4, 9 27 P(x, y)- 0.

A: Two dimensional random variable is said to be discrete when it takes at most a finite number of…

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: 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: 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: 20) Let f, g E F(R,R) be the functions defined by f(t) = et and g(t) = est,r ± S. Prove that f and g…

A: Answer

Q: Consider the operator T: 1 defined by a = whether the following statements are true or false. (1,…

A: In Codomain only first term of domain will be exclude.  Hence,  null space will be (a, 0,0,.....)…

Q: Ques. 3: Check whether the operator T: R2 → R2 defined by T(x, y) = (y,x) is linear. Moreover if T…

A: A mapping T:R2→R2 is a linear transformation if and only if a) T(u)+T(v) = T(u+v) b) T(cu) = cT(u)…

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

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Q: Let T: R3 → R³ defined as T (x,y, z) = (x,x – y, 2x – z). Then adjoint operator T* (u, v, w) is A.…

A: We have to find the adjoint operator T*.   According to our guidelines we can solve only 1 question…

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: Let T be function from R to R de fined as T (x) = r2, where a (x1, 2) %3D Then show that iST…

A: Let T:ℝ2→ℝ be a function defined by  Tx=x2 where x=x1,x2 To verify whether T is a linear operator or…

Q: (b) If f is a bounded linear functional on a Hilbert space H, show that there is a unique y e H such…

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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…