Problem 2: Let V be the vector space of polynomials in t of degree < 3 and let o: V V a linear operator given by ø(f(t)) = f'(t) – f"(t). (1) Find the matrix [ø]e with respect to the basis e = (1,t, t², t³) of V. (2) Find the kernel and the image of ø.

Q: V(3278)3 + 6230 – 12e90i

A:

Q: (4) y=x +4 -5 -4 -3 6.

A: The given equation is: y=x+4

Q: 10 14 9.) Find O 18

A:

Q: 1.25a +3> 0.5a-6 and 2.5a 129-1.5a

A:

Q: A-1 does not exist.

A:

Q: xp xペ-4xt13

A:

Q: 9 – 4x > –3

A: The given inequality is 9-4x&gt;-3

Q: If A: find A 2. 3 3. and Show Shat A-3

A: A=1213 Now determinant value is, A=13-12=1 Adjoint of matrix A is, adjA=3-2-11 Now,…

Q: х3 — 2х dx х — 1 -3 10. 2

A: Given: I=∫23x3-2xx-1dx For evaluating given integral, we substitute x-1=t…

Q: +–3m+–9m+4+5+–10m

A: The expression is given as 1+–3m+–9m+4+5+–10m. Simplifying the given expression. 1+–3m+–9m+4+5+–10m…

Q: 18) 2x y

A:

Q: Find A.

A:

Q: Evaluate. (3- 5)² + 4(1 – 5)

A: Given, (3-5)2 + 4(1-5)

Q: 5)235

A: Answer : 47

Q: Find the LU factorization of A = A = 1 1 -3 0 9 3 -17 5 2

A:

Q: 2070 = (16a + 10)15

A: 2070 = (16a+10)15 And (16e+11)17 =3723 To find  the values of a and e

Q: Solve using method of undetermined coefficients: y" + y' - 2y = x². %3D

A: Solution :-

Q: 9. (x² – 2)3

A:

Q: 1 + 2n < n° for all integers n² 2

A:

Q: y27x+2

A: y &gt;= 7x/4 +2

Q: Identify the work done, J. F.dr by an electric field, E = (x + xy)î + (y + 5)f – 5zk V/m to move an…

A: Work done along the curve C by vector field F . Where C is given by parametric equation r(t)…

Q: Find A3 if A = {1, 2, a, b}

A: Given,      A=1, 2, a, b

Q: Evalvate S (4sin co) -8cos co) )do

A: Given that: ∫0π(4sinθ-8cosθ)dθ

Q: (1– 3csc(

A:

Q: S√4 4+² +3 dt

A:

Q: 75 + フチ + k「3

A:

Q: –4(–6m – 7).

A:

Q: 3. (x³ + 4x² –x – 1) + (x + 3)

A: Here we have to divide two polynomials as shown.

Q: いーx)dx

A:

Q: 2. (1 + 3/2x − 1)² = 3 + √3/2x − 1

A:

Q: 4 -3 4m n 16) 22 4m n

A:

Q: -96 6 -7 A = -3 d 4A.

A:

Q: (2n)! 323. 2n

A:

Q: 7. (2x + y)³

A:

Q: x + 4x +16x + V... + V4"x+3 – Vx = 1

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.