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 2/3

Q: Find the dual of the Boolean expression T+r.0+ ryz O T.(T+0). (T +y+ z) O r. (r.1). (T + y+ z) O…

A: The dual of Boolean expression is given as follows :

Q: Give the demains of and the corresPonding domainsof E+9€F-9+F-9F/9rand/f For the fallowing 2 Fw =…

A: To find the domain of each function

Q: Use a table to express the values o

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Q: Find of the function x³ z2 – 5æyz = a? + y %3D

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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: I| (2 + x²y)dA, R = [0, 1] × [–1, 1]

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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: Let A and B be two sets and f be function. f: A B.Assuming the function f is invertible, what is the…

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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: ○A. T(A) = 3A from R6×4 to R6×4 -9 9 B.T(A) = A [72] [173] 4 5 ASA-¹ from R2×2 to R²×2, where S A…

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Q: 1 1 2.- 2. Is b₁ = 2 in the null space of A=-1 L-3] 1 -1 1 1 -1? What about b₂ -1 1 ГО =6?

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Q: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: 1. Answer all parts. (a) Consider the operators A and B. Show that (i) (ii) [A, B]=-[A, B] [Am, A"]=…

A: Operators :A and B

Q: Let i = (– 4, 4, 5) and i = (6, – 3, – 2). %3D • Hint

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Q: -1 2 1 Let A Compute AAT and AT A. 1 0 1 1 -1

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Q: 1. Let Q(v2) = {a+b/2| a, b E Q}. Prove that Q(/2) = Q[x]/(x² – 2).

A: We have to show that isomorphism means there is function ϕ such that we have to show that it is an…

Q: Given u(x)= x +3 and v(x)= 9x – 4, find u v. O 9x² – 12 - O 9x² + 27x – 4 O 9x+ 23 x - 12 O 9x + 23…

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Q: Express y as a fiunetion af k if y - 2r+5, 1- V3t -1, and t- 3k - 5.

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Q: Find the norm of f(x) = √√1-x² on the interval [- 1,1]. 2√3 3 O O O W|N H

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Q: Let G = Z5®U(7). The identity of G is %3D (1, 1) (0, 0) O (0, 1) None of the choices O (1, 0)

A: Use the property of external direct product to find the identity of the group G.

Q: Let Ps have the inner product given by evaluation at-2,-1, 0,1, and 2. Let p(t) = t2- 2t and q(t) =…

A: Let P3 have the inner product given by evaluation at -2, -1, 0, 1 and 2 . Let p(t) = t2-2t  and q(t)…

Q: Find the norm of f(x) = √√1-x² on the interval [- 1, 1] . √3 a|m O 2 P 3 2√3 3 2

A: A norm is a function that assigns a non-negative length or size to each vector in a vector space.…

Q: Q.4.(a). Show that the following functions is not an inner product on R3, where u = (u, U2, U3) and…

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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: Let f.g.h:A - A be any bijective functions. Then (g oh on-

A: (g∘h∘f)-1=f-1∘h-1∘g-1 composition of function is associative…

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: 5d rd-2a 2b a D. 5e-h If det d Lg h i 1, compute det e If - 2c %3D C 5f-

A: To compute determinant of the given matrix.

Q: Let y = Ա 4 + DIS 5 Ա and u = x³ = x³ - 2x.

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Q: Let A = 1 X I 2 X 3 X x² 1 1 x 1 I ,2 Ꮖ ; Find a such that det (A) = 0.

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Q: 3. Determine whether each of the following functions is a bijection and explain why. (a) f: R R,…

A: Note:As our company  guidelines we are supposed to answer only first 3 sub-parts. kindly re-post…

Q: -3 and y = 2 0 Let x = ||x - y||₁ ||x - yl|oo = ||x - y||2₂ = 3. Compute

A: Given : x=-5-32    , y=330

Q: Recall that for D a squarefree integer, the norm function N on Q[VD] is defined by N(a + bVD) = (a +…

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Q: Let fi = 1+x + x² + x³ , f2 = 1 + 2x + 3x? + 6x³, f3 = 3+2x + ? + 5x4, and g = 1+x + 2a? + tæ³. For…

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Q: Let y = 7 and U-span(u), with u = x1 = x2 = -21 TT -4. Write y=x1 + x2, where x1 in U and x2 in U+.…

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