Let T be function from R to R2 de fined as T (x) = (0, x), Then show that if T is linear operator or not

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

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

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

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

A: ANSWER :

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

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Q: Are the functions f(x) = e ^x and g(x) = e ^|x| linearly independent on I = (−1, 1)? Are they…

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

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

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Q: Let f, g, ϵ F (R , R) be the functions defined by f (t) = ert and g(t) =est, where    r ≠ s. Prove…

A: We can prove this question by the contradiction method, So, Assume that the opposite. Let {f, g}…

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

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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: Let T : R3 → R² be a linear mapping. 2 .T Given that T and T find T

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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 0 -1 0 0 Determine whether T is decomposable or…

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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: Let L:R3 → R3 be a linear operator such that L ×2 X1 then Ker(L) spanned by: X3 Select one: O a.…

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Q: Consider the functions f(x, y, z, t) = (x² + 2. t²) and g(u. v) = (uy, u +v. u – v). Use the chain r

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

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Q: 8. Show that an isometric linear operator T: H→→ H satisfies T*T= I, where I is the identity…

A: Let T : H → H  be an isometric linear operator. We need to show that , T satisfies T* T = I We know…

Q: Let L be the line in R2 through the points [:][] and Find a linear functional fand a real number d…

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Q: Let f1(x) = 3x and f2(x) = ∣x∣. Graph both functions on the interval −2 ≤ x ≤ 2. Show that these…

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

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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: 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.…

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Q: Let g(x) 8 In(t) dt. Use the Fundamental Theorem of Calculus tc g'(x) =

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Q: The Wronskian has been computed. Determine whether the functions are linearly independent or…

A: Here given the wronskian of function ex and 2ex is zero.

Q: Let T be function from R to R² de fined as T (x) = (x, 0), Then show that if T is linear operator or…

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Q: Q NO 3 Let T: P2(R) → P2(R) be a linear operator such that T(1) = 0, T(1+ x) = 1 and T(1+ x²) = 2x.…

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Q: Consider the operator T: 1 given by T(r1, 22,. ) = (0, r1, 22,. ). Is T a compact operator? Explain…

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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…

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: Use the Wronskian to show that the given functions are linearly independent on the given interval I.…

A: For linearly independent, we show Wronskian is non -zero.

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