2. Let V be the set of all ordered pairs of real numbers, and consider the following addition and scalar multiplication op- erations on u= (u1, U₂) and v (V₁, V₂): u+v= (u₁ + v₁ + 1, U₂ + V₂ + 1), ku= (ku₁, ku₂) www. (d) Show that Axiom 5 holds by producing an ordered pair 1 -u such that u + (-u) = 0 for u = (u1, U₂). (e) Find two vector space axioms that fail to hold.

Q: Operation o additien for all (XuX), (XXanXa) E TR. Define an operation fScalar multiplication…

A: consider a set S on ℝ2 where define an operation of addition on ℝ2 by X1,Y1*X2,Y2=X1+X2+1,Y1+Y2+1…

Q: Let ū = (-1,2,4) and ū = (-3,5, 2). Compute the following: (a) ū+ū (b) .공 (c) ||해 (d) ũ - 7 (this is…

A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

Q: Prove that Cov (x, y) = E (xy) – E (x) E (y).

A: Cov(x,y) is covariance of x and y. E(x) is expected value of x E(y) is expected value of y.

Q: u = 3i – 2 j+4k v=i-3j-k 18) (Section 9.7) Find the cross product in space i j KI 3 -2 4 -3 -1|

A:

Q: Let Ai = {i, i + 1, i + 2, . . .} find ∩∞(infitity)i=1Ai and ∪∞(infinity)=1Ai Explain.

A: We have to find the intersection and Union of given set.

Q: 4 7 2 Let M-[and A-and-]-[3] B= 7 Express M as a linear combination of A and B and C 1) M=3A-2B+C 2)…

A: Given that the matrices  M=4779 , A=1111   , B=1234  and C=1145 .

Q: Let V be the set of all ordered pairs of real numbers under the following operations of addition 1.…

A:

Q: Given the vector (x <- c(5, 2, 7), what would x^2 return? O [1] 78 O [1] 196 O [1] 25 4 49 O [1] 10…

A: Given that, the vector is        ,we need to find .

Q: Prove in detail that ℚ(√3+√7) = ℚ(√3,√7).

A:

Q: Prov that Let A be a fuzzy ideal of R, anand by Lemma- be fuzzy singletons. Then (a.b) no A = anobu…

A: To prove that (a⋅b)h ⋅A=ah ⋅bh ⋅A given A is a fuzzy ideal of R and ah , bh are fuzzy singletons, we…

Q: Assume that n(U)=115n(U)=115, n(B′)=65n(B′)=65, n(A∩B′)=32n(A∩B′)=32, and n(A∩B)=19n(A∩B)=19 Find…

A: Now consider,

Q: What is the coefficient What is the coefficient of rx3x3 in (x₁ + x2 + x3 − x4 - x5)⁹? 1 13 of 2¹3…

A: To find the coefficient of x14 x32 x43 in (x1+x2+x3-x4-x5)9 we will use binomial theorem.  The…

Q: Let u = (-7, 1, 5) and 7 = (5, 3, 4). —

A:

Q: Let ---0--0 8 u= W= Compute 3w+6u = -131

A:

Q: Question: Show that the set Pn of all polynomials with real coefficients of degree n is a linear…

A:

Q: Prove from fundamental definitions and principles, that (-00, 0] and (0, 4] are numerically…

A:

Q: 7

A:

Q: 9. Let V be the set of all ordered pairs of real numbers, and consider the following addition and…

A:

Q: Suppose J3 is derived from switching the rows of 13. -5 3 0 -8-1 7 -4 If AJ3 = 0 -2 7 -2 3 -5 -8 or…

A: NOTE: Refresh your page if you can't see any equations. . the 3×3 identity matrix is given by now…