SECTION A: SHORT ANSWERS Question 1 Let U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A= {x|x is a positive integer and+2 4, B-(2,4, 6, 8, 10}, C= {2,3, 5, 7} and D (1, 5, 10}. Find the valué for each of the operation below: (а) (AN B) - C (b) A'OB (c) (AnC)8 (BU C) (d). P(D) (e) P(D)

Q: et a =i- 2j + k and b= 2i+j +k. Show that la + b| s lal + b|

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Q: If A and B can be placed in a one-to-one correspondence, must A=B?

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Q: Find the solution to this recursive relation an = an-1+3, a0=1

A: To Find the solution to this recursive relation an = an-1+3, a0=1

Q: How many individual simple functions make up the following composite input? 2 1 5 6 A) 4 в) 5 c) 6…

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Q: Find all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1 1 1. A = 1 3 1. 1 -2 2 4 21 C li 3…

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Q: - 25х-1 dt 2*

A: Consider ∫25x-12xdx = ∫25x 2-12xdx= ∫25x-x2dx= 12∫24xdx                                     (1) Let…

Q: Example 7.4.1. If a = (2, -1, 3) and b (1,2, 1), find a x b.

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Q: Find the values of a such that det (² 3-x 2 3-x 4 1 -1 -1-x = 0.

A: We have to find the value of x such thatWe know that

Q: What is the domain of the following: y = 3x? * 0 02 O 3 O-1 O-2 O -3 all real numbers O x >=0

A: as per the company rules we are supposed to answer only the first question and rest others can be…

Q: (b) Let A¡ = [-i, 1] for every positive integer i. Find U A¡ and N1 Aj.

A: Given that Ai=-i,1 for every positive integer i. That is, A1=-1,1, A2=-2,1, A3=-3,1 and so on. To…

Q: Find the following products for P (7,0,2), q = (-2,2,-2), 7 = (0,2,-3) (F. P)a

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Q: A [(0,6) U (7, 12)]n (2,9; B= A\({1,2, 4} U (3, 5)) and C = BU{11, 8}. Give an explicit and fully…

A: This is a problem of point-set topology.

Q: Find a given that ||a i+ (a – 1)j + (a + 1)k|| = 7.

A: Given:

Q: If A = {2,3} and B = {x|x EZ, x<3}, then A x B = Select one: O a. {(1,2), (1, 3), (2, 2), (2,3)} O…

A: If A=2, 3 and B=x x∈Z+, x&lt;3, then to determine A×B.

Q: H.W 1.: Use Cayley-Hamilton to find 4 -1 A' and A Where A = [2 1 1 0 1 0 11 2 ]

A: Find characteristics polynomial and use caylay hamilton theorem

Q: 31. Letf(x) = [x²/3]. Find f(S) if a) S = (-2,-1, 0, 1, 2, 3). b) S = {0, 1, 2, 3, 4, 5). c) S = {1,…

A: 31. Given the function is                            f(x)=x23.

Q: {1,3, 5, 7, 9, 11}. Use the Let X = {4, 5, 6, 7, 8, 9} and Y roster method to describe each of the…

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Q: At which angle is cos=-1?

A: Given cosθ=-1

Q: Let = [1, -1, 1], [-2, -1, 3] and = [-1, 2, 2]. Find (u ×7)•w: O-14 07 O 10 Does not exist

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Q: Q1) Find the inverse of A (1 00 A=2 1 0 5 4 1

A: A=100210541

Q: tan(z1) 0.9947 + 0.1462i 0.0364 1.0047i

A: The definition of tangent function for complex number is tanz=e2iz-1i(e2iz+1). Use 4-2i for z1 and…

Q: Find u x v, v x u, and v x v.

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Q: 1 2 and B ol: Compute the following: 2A, A – B, AB, and BA. Let A -3 1

A: Given problem:-

Q: 4. Find z, and z, such that, 2iz, +iz, 2+5i and = 9-11i 3i z,-2i 2, 4 =i+1, z, = 3+4i (b) z, = 3-4i,…

A: Solution:- let z1 and z2 be the different ccmplex number i2= -1 i3=-i

Q: .

A: Given

Q: Find all the values of z for which 1+z 1 1 1 1 1+z 1 1 1 1 1+z 1 1 1 1 1+z 0.

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Q: In R, we can explore the values of a single column. For example, the first 10 values of Sepal.Length…

A: In R, we can explore the values of a single column. the first 10 values of Sepal.Length (the first…

Q: -1 Let A = 01. Compute A100 -2 1 1 3.

A: To compute the A100 first we need to diagonalize it to make the computation very easy.

Q: -2 1 2 -1 1 -1 2. LetA= Then find A-1 if it exist. 1

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Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

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Q: Let 4 1 - 3 -2 -9 and 1 A =| - 3 В C =| 0 3 Prove that 5 - 2 -1 1 1 – 4 | (BA)" – A" B" + AC = AC,…

A: (BA)T - ATBT + AC = AC In LHS, We know that, By the properties of Transpose, (BA)T = ATBT .…