3. Let V be the set of all ordered triple in R³, and F, the set of real numbers, where the operations are defined as follows: : (X₁, X2, X3) + (V₁, V2,Y3) = (X₁+ Y₁, X2+Y2, X3+ Y3) : C (X₁, X₂, X3) = (CX₁,CX2,CX3) Prove that V is a vector space.

Q: Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R² R², T(x, y) = (2y,…

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Q: Let the domain of x and y be all people, Let W(x): "X is a woman". M(y): "y is a man", and L(x.y):…

A: Given W(x): ' x is a woman' M(y):' y is a man'

Q: Let F= R and V = R*. Let W, = {(x1,x2,X3,X4) € R* : x1 – x2 + X3 – x4 = 0 and x1 +x2 = 0}, W2 =…

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Q: evaluate the Pirst and second deriugive of f) = 327+5csin 3x• %3D at x= 11 , 2.5 &3.7

A: To evaluate the first and second derivatives of f(x)

Q: Let u = (2,6, 4) and 7 = (-1, -2, - 7). Compute the following: ū. v = vu - ||||²

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: For the predicate P(x, y) ::= [x + 2 = y], choose all the pairs of x and y such that P(x, y) is…

A: Given query is to find the correct option for the expression.

Q: Prove that (ab + cd)² ≤ (a² + c²)(b² + ď²) for all a, b, c, d ɛ R.

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Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

Q: d) Prove (AV (Vx) BC = (Vx)B(AV C), as long as x not free in A. (Hint: Translate first to Standard…

A: Given,  Prove (AV (Vx)BC = (Vx)b(A V C), as long as x not free in A. (Hint: Translate first…

Q: (Q. +,.) is a subfield of (F = {a + bV5: a, b e Q}, +,.); (F = {a + bv5: a, b e Q}, +,.) is a…

A: A non-empty subset F' of a field F is a subfield of F if F' is closed with respect to the…

Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

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Q: If f(x1,..,x „,0) = g(6,0) h(x,..,x„), then ê® is Select one: a. sufficient b. efficient C.…

A: Introduction :-  We have to select most correct option for the given statement. Basically it is a…

Q: If o = (r x a) (r x b), show that Vo =bx (r x a) +a x (r x b)

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Q: Eliminate A and B from the relation y = Ae²x + Bxe²x

A: Given:y=Ae2x+Bxe2x...................(1)

Q: What’s (E∩F)×(F∪G)

A: We are given that E = {1, 2}, F = {2, 3} and G = {3, 4}.Now, E∩F = {2} and F∪G = {2, 3, 4}.

Q: Given sets X, Y and Z, use the set properties to show that (Z – X) n (Z - Y) = Z (XU Y), indicate…

A:

Q: If A has a row or column consisting entirely of zeros, then Select one: a. A is nonsingular b. A is…

A: Given: A is row or column consisting entirely of zeros .

Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- 1 x² - y² (x² + y²)² X x² +…

A: The number is 1z2 where z=x+iy

Q: Let u = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

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Q: 2. Evaluate: √₁² √2 - x + x da −

A: We know that the modulus function fx=x is defined as x=-x,x&lt;0xx≥0. If we take x=-2, then f-2=2…

Q: Let the domain of x and y be all people. Let W(x): "x is a woman", M(y): "y is a man", and Lex.y):…

A: The objective is explain the meaning of the statement ∀x∀y Wx∧My→Lx,y

Q: Let Q(x, y) be the statement "x + y = x - y." If the domain for both variables consists of all…

A:

Q: Find a pair of values (x, y) that serve as a counter-example for the statement that [ry] : |x||y for…

A: The ceiling function gives smallest integer that is greater than the number, that is, x is the…

Q: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

Q: Set f(a,b) = (1+ a + b) + (2 + 2a + b)x + (1 + a + 26)r² and F = {f(a, b) : a,b e R} a subset of…

A: Given that fa,b=1+a+b+2+2a+bx+1+a+2bx2 and F=fa,b : a,b∈ℝ is a subset of ℝ2x. The objective is to…

Q: If (x, y) what is G ()? 3x-5y {c}= {D} - -18 {A } 67 6 -15 {B } 67 6'

A: Given; 1) 3&lt;=x&lt;5 2) (x,y)=2x/(3x-5y).

Q: If x and y are both less then 0 and xy

A: Given, x and y are less than 0. Then xy = ?

Q: Let z₁ = 7 - ni, 2₂=2 m+ 3 i, and Z3=4-7 i If 2 Z₁ + Z₂ + 2 z3 = 28+5 i,find m and n: m n=

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Q: Q1: Determine if a +b+c+d=10 where a, b, c, d ER are such that: 6x³+3x²-5 -1 2a x-l + 3b x+1 + cz…

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Q: Q closed over multiplication? (Y/N) 6. Is N closed over multiplication? (Y/N)

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Q: The functions h and m are defined on the set R of real numbers by h:x→ ax +b and m:x → cx -d, where…

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Q: Let A {a, b} and B = {1, 2}. Give an element of A x B x A.

A: Let M and N be two sets. The Cartesian product, M×N is the set of all possible ordered pairs with…

Q: Use Cramer's rule to find only the value of x2 , where a is a positive real number. 2x2 – x3 + x4 =…

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Q: Find 1 L L 0 0 (3x + 2y) dxdy

A: