3) Compute the gcd of T³ +T2 +T+1 and T4 +T³ – T² +1 in (Z/3)[T].

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: Define a linear transformation T:P3>P3 by T(p) = p(0) + p(2)t – p(0) t²- p(2) t³ Is p eigenvector…

A: Given that  Linear transformation T : p3 → p3 Defined by, T(p(t)) = p(0) + p(2) t - p(0) t2 - p(2)…

Q: A linear operator T: P2 P2 is defined as T(p(x)) = p(2x+1), i.e. T(c + c₁x + c₂x²) = C₁ + c₁ (2x +…

A: Here T is given linear operator from P2 to P2. First we have to find matrix TB of T with respect to…

Q: Find the standard matrix of the linear mapping L ab sin (a) f Əx ∞ α 52 5 2 x2 23. [2271²-1472²7223]

A:

Q: assume that Pr[A]=0.25Pr[A]=0.25, Pr[B]=0.35Pr[B]=0.35, and Pr[A∩B]=0.1Pr[A∩B]=0.1. 1)Pr[A|B] =…

A: Given: P(A) =0.25 P(B)=0.35 P(A∩B) =0.1

Q: Let f(T) and g(T) be polynomials in Q[T] whose gcd in Q[T] is 1. Show that 1 is also their gcd in…

A:

Q: 4) Which of the following functions are eigen functions of the operator dx ? Show your proof. a) eax…

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

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

A:

Q: Consider the linear transformation T : R2[x] → R2[x] given by T(a + bx + cx2 ) = (a − b − 2c) + (b +…

A:

Q: Compute [GL2 (R): SL₂(R)].

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

Q: Suppose that a linear mapping S(x1, x2) = (t₁x1, t2x2) satisfies S *([4]) = [2] Compute the standard…

A:

Q: Define T by T: Pn → Pn-k by T(p) = dk p(x) dxk 9 where P is the set of all polynomials whose degree…

A:

Q: Find the kernel for the transformation T(x) = Ax if ? = [1  2   0   1 −1]       |2   1   3   1   0|…

A: We have to find the kernel for the transformation T(x)=Ax if:…

Q: Define T by T: Pn → R by T(p) = =S² p(x) dx, where P is the set of all polynomials whose degree less…

A:

Q: Let T: P→ P3 be the linear transformation satisfying T(1) 32²7, T(x)=-3x+8, T(x²) = 2x² + x +4. Find…

A:

Q: Exercise 4.3. Consider f = 3x“ + 2x +2 and g u and v such that fu + gv = gcd(f,g). = x° + 2x +1 in…

A:

Q: Find a zero-divisor in Z,[i] = {a + bi | a, b E Z3}.

A:

Q: Show that f(x) = x³ + 2x + 20 is irreducible over Q.

A: We say that a polynomial is irreducible if it cannot be expressed as a product of two non-constant…

Q: 21. Show that the set of polynomials {C₁, C₂ (2x - 1), C3 (6x² − 6x + 1)} in P(R) is orthogonal with…

A:

Q: Let f(x, y) = In(x²y), where a = s² + t² and y = 2s + 3t. %3D Which of the following is a correct…

A: Given,           f(x,y) = lnx2y3,  where x = s2 + t2 and y = 2s + 3t

Q: 1) Find the inner product (f.j) between the following pairs of functions fands. part a) f and are…

A: Step 1: