Let T: M22 → P₂ be defined by T T([1]) ¹([8]) T([1₂8]) T([i]) −3x² + (−1)x+ (1). :52+(−1)2+(1) MDB (T) = b₁ Choose the ordered bases B of M₂2 and D of P₂ such that [1 0 0 0] 0 1 0 0 0000 b₂ = b3 = B = {b₁,b₂, b3, b4 } where [1] [J] -1 0 b4 10 O = and D || = -1 (a 1x² + 1x - 1. = 1x² -1x + 1. =

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

Q: f= (2xy+ 3x²)ē+ (x² – 2yz + 2y)ē, – (e² + y²)ēz

A: Given

Q: Compute the convolution L ★ II of the functions L and II, which are defined below: 1 if |æ| <a/2…

A: For the function, Lx and πx, Convolution of Lx and πx can be calculated by L∗πx=∫0x Lt πx-t…

Q: 3) Let f(T) e R[T] be a polynomial of degree > 3. Show that there exists polynomials g(T) and h(T)…

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Q: Show that the function a Y1 (x, y) = [21 2] в с Y2 is an inner product on R? if and only if b2 – ac…

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Q: Prove that if Xn X and Ync, then (Xn, Yn) → (X, c).

A: Please see the answer innext step

Q: Let X=ℝ2 and define d,:ℝ2×ℝ2→ℝ d2((x1 ,y1),(x2,y)2)) = max{|x1 - x2|,|y1 - y2|}. Draw the…

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Q: Let p be a prime and let q = p". Let f(x) = x³+ax+b € Fq[x] be

A:

Q: Suppose S, T € L(V) are such that ST = TS. Prove that N(S) and R(S) are invariant under T.

A: It is given that S,T∈ℒV are such that ST=TS. It can be observed that for any v∈NS, Sv=0. Since,…

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A: Here we have to find the Laplace transform.

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A:

Q: Let x(t)=5sinc(1.5t) +6cos(7/2) and h(t)=4sind(). Determine y(t)=x(t)*h(t) using Fourier Transform…

A: Let  and We need to determine y(t)=x(t)∗h(t).To solve this problem, we list the Fourier transforms…

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Q: 9-12s-4s2 C. (s2+4)2 +12s-2s2 (s2+4)2 9+12s-4s? D. (s2+4)3 -12s-2s? (s2+4)3

A:

Q: Find the laplace transform of t sin (t) A. 2s/(s2+1)2 B. 1/s2(s2+1) C. 1/s2 + 1/s2+1 D. -…

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Q: Show that the following polynomials are irreducible over Z[r]. fi(x) = 17r³ + 7x + 3, f2(r) = 2r* +…

A: Using the result: A polynomial of degree 2 or 3 is reducible over the field F if and only if it has…

Q: Let A be invertible. Prove that At is invertible and (At)−1 = (A−1)t.

A: Given:Let A be invertible. Prove that AT is invertible and (AT)−1 = (A−1) T.

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.

A:

Q: b₁ + x b₂ + x b3 + x + +x\ C₂+x, then show that A'(x) = 0 a₁ + x If A(x) = a₂ + x a3 + x C3 + x and…

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Q: Show that f(x)= x14 – 6x + 75 is irreducible over Q.

A: Eisenstein's Irreducibility Criterion: Let us consider polynomial…

Q: Q[V2 ]is Principal Ideal Domain..

A: Q[√2] is Principal Ideal Domain. True.

Q: Derive the following Fourier transform: cos (2Nfot +0) ½ [8 (f + fo)e® + & (f - fo)e® ]

A:

Q: Prove using the generating function of the Legendre Polynomials: t2 [xP(x) – nP,(x)]t": (1- 2xt +…

A: We have to prove ∑n=0∞xPn'(x)-nPn(x)tn=t21-2xt+t232 We know the generating function of the Legendre…

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A: We will use GRAM-SCHMIDT ORTHOGONALIZATION PROCESS to solve this problem For a basis y0,y1,y2 to…

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Q: 1 5 -3] Question#3: Let A =|-1 7 1, b = and -2 4 0 T:R³ - R' be a transoformation defined by T'(x) =…

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