Let L: R -R be defined by ()- -2 -1 L 3 2 2 1 1. Show that L is invertible. (E) 2. Find L

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: 0 0 0 1 0 0 0 1 0 ) Let A =

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Q: 6: F7 → F2 where (x1, x2,...,x7) = (X1 + X2, X3 + x7). Prove is not a linear functional on F7

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Q: Find the fourier transform of the following. functions by making use of Jordan's Lemma. a) 1 (x² +…

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Q: 3. The linear operator T: R³ R³ is defined by T(x1, x2, x3) = (W1₁, W2, W3), where w₁ = 2x₁ + 4x2 +…

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Q: [X1 X2 4) If A X3 [x4. 1 find all the unknowns using Cramer's rule. |0 -1 -2 -3 -41 1 Let A = 3 6 5…

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Q: Why is inversion [that is, (x, y) = (-x, -y)] not listed as one of the four kinds of isometries in…

A: We have to tell, Why is inversion [that is, ϕx,y=-x, -y] not listed as one of the four kinds of…

Q: 2. Consider the Newton polynomial Pn(z)= ao+a1 (1-10) + a₂(1-10) (1-11)+... +an(1-10)(1-1₁).…

A: Given that   that interpolate then we have Now  ,       putting

Q: (5) Consider the two functions f, g :R –→R defined by the formulas f(x) = 3x+1 and g(x) =5x² – 10…

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Q: Let G : R? → R³ and F : R³ → Rª be defined by G( (x, y)) F( (a,b, c) ) (x +y, x – y, 2y) (a + b+ c,…

A: Given G:R2→R3 is defined as Gx,y=x+y,x-y,2y Also,  F:R3→R4 defined by Fa,b,c=a+b+c,2a+c,b+2c,a+b.

Q: 3. Consider the following data set -2012 f(x₂) 5 1 -1 5 (a) Construct the quadratic Lagrange…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

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Q: Let TA an operator from R2 to R2. W(w1, w2) = TĄ(X1, x2) W1 = -2X1 + 6x2 W2 = 3X1 + 1X2 if TA is…

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Q: Ax = b must have a solution for eac In Exercises 33 and 34, T is a linear transformation from R2…

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Q: 2. Let T: P2(R) → R³ and 4 2 [T]; 1 1 1 where B = {1, x, x²} and y = Is T invertible? {(1,0,0), (0,…

A: The solution is given as

Q: [X2 - X1] X3 - X2 , then L( o D= X3- X1 X1 1 Let L:R3 → R be a linear operator such that L( x2 X3…

A: L x1x2x3= x2-x1x3-xx3-x1given linear operator on R3

Q: Q2: Let T₁, T₂, be the following bounded linear operators ¹ → T₁(x₁, x₂. x3,) = (x₁, X₁, X₁, X₁,…

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Q: Compute [GL2 (R): SL₂(R)].

A: To find: The value of GL2ℝ : SL2ℝ .

Q: prove that theta(2m) = theta(m) when m is odd and theta(2m) = 2 theta(m) when m is even

A: We can start by using the definition of theta notation to prove these statements. Recall that theta…

Q: 4. Let L: R² → R? be a linear operator. If L((1, 2)") = (-2, 3)" and L((1, – 1)") = (5, 2)" find the…

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Q: Let Te B(H) be an invertible operator. Show that a(T-) = 0(T)-.

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Q: Given that f is a polynomial of degree n in Pn, show that { f, f', f'', . . . , f(n)} is a basis for…

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Q: Show that the function f:R –R givenby f(x) = log, (x+vx* +1),a>o,a±1. is invertible and find its…

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Q: EHET X1 X2 - X1 Let L:R3 → R³ be a linear operator such that L( x2 ) =| x3- X3 - X2 , then Ker(L)…

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

A: we know that Ker(L) is solution of the system L(X)=0  Reveal sold the system and find the ker(L)…

Q: Suppose L: R² R² is defined by L ordered bases. [L(u)]B₁ = [L(u)]₂ 4 [X₂] - [ × ₂ -³X₁ ] . Let B₁ =…

A: Let  is defined by .Let  and  be ordered basis of .Given .We need to find  and .

Q: Integral Representation for ₂F₁ : T(c) = a T (b) T (c − b) √ ¹b-¹ (1 - ₁)²-b-1 (1 − xt)¯ª di 2 F₁…

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Q: (20) Prove or give a counter example. Let f: A → B and g: B → C. If go f is invertible then…

A: We have to prove the given theorem.