Suppose that B is a point between A and C. Prove that AB−→ =AC−→

Q: Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

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Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: Verify that (AB)T = BTAT.

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Q: Prove that if Xn X and Ync, then (Xn, Yn) → (X, c).

A: Please see the answer innext step

Q: Say that E = Ãek™, where the components of A and k are real and constant, i.e. they aren't imaginary…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

Q: Suppose RC 1. prove that if B has a sup b, then A(U(B))

A: Given:- Suppose B⊂A and to be proved if B has a Sup b, then λ(ϑ(B))∩ϑ(B)=b

Q: Give the condition which ensure that Je-| < 1 where z E C.

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Q: Use De moivres theorem to determine (3-4))"C4cis 30° )ieave your answer in 10 CiS the Formof Fciso

A: According to the given information it is required to determine the value of

Q: Find the fowien senies fon | X), -T<X <A

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Q: Given u(x, t) = t-²e¯, 2 , compute:

A: We can find the required answer as below.

Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

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Q: Suppose that x̅ = 12, Sx = 2, and z is 1. what is X?

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Q: prove using the IVT. √c +√c + 2 = 3 has a solution.

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Q: verify that (A + B)T = AT + BT

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Q: Let x, y EZ. Prove that 3|xy if and only if 3|x x or 3 y.

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Q: Suppose that a linear transförmation / satisfies T(u,) = T(u,) = -1 -2 Find T(4u, - 3u,). T(4u, -…

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Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.

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Q: Prove using the IVT. 2x = bx has a solution if b &gt; 2.

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Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

Q: Prove that ifx > 3 and y> 4, then xy > 11.

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Q: Find the of im < Re z< £ un der w-

A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…

Q: Prove that, IXI<a Rf and If -aL X Z a

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Q: Let x, y € R" be given. (a) If ||z||||y||=1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1 and ||y||…

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Q: (a) Prove that de 2n a>b>0 Jo a+ bcose Ja? - b2

A: We will use basic knowledge of Integral Calculus and trigonometric identities to solve this…

Q: Exercise 2. Prove that if A = B and C z D, then A × C = B x D.

A: Given data: A≈B......(1)C≈D......(2) The objective is to prove A×C=B×D

Q: Solve the following first-order linear DE's. yE) = 1 y' + (cotx)y = xcscx, %3D

A: Proceed as shown below

Q: Let f(x, y, z) = x³ – yz?. Find af af of and ax' dy az

A: Given : fx,y,z = x3-yz2

Q: If xly, then show that ||x+ y|| = ||x- y|!.

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Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: Prove: For allintegers aandb, if a|b then a² |b²

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Q: Express E: livenr coumbination of Ÿ; = and V as a

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Q: SHOW that V Ź a? Jor a, E IR when His ineguaity e kold .

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Q: If x<y, prove that x<(x+y)/2<y?

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Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: If (a + bx)e = x, prove that x’y, =(xy,-y)

A: Since you have asked multiple questions , we will solve first question for you. If you want any…

Q: 1. If x, y, z E R, prove that (a) \x+y\ < \x| + \yl- (b) |x– y| < |x – z|+|z– y|, and (c) ||지| -…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y4…

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Q: If (x* – y*,x – z°) = 0,z = z(x, y), prove: az y3 az +x³z4 ax - %3D ду 3

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Q: 3. If u= (x+y +z') , prove that +y

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Q: Selve the fallowing euler Cauchy.eg:using net hed of variation? O xy.3x y+ 6X.y-6y= Xs,in X 2. %3D

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: Prove that du Inlul + C where n= -1 u

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Q: Prove that (A = B) where (A = ax + ay + az) and (B = bx + by + bz)?

A: Given- A=ax+ay+az and B=bx+by+bz To Prove- That A=B

Q: Show that if A and B are similar, then AT and BT are similar.

A: Let A and B are similar matrices. By definition of the similar matrices.  The matric A and B are…

Q: Select all the Points through which a unique solution for the DE ,2 y? IS nySot eed by the Existence…

A: Given differential equation is y'=13-x2-y2

Q: Let S = {(x, y) :x² + (y – 1)² < 1} U {(3,0)}. %3D Is the origin an extreme point of conv S? Is the…

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Q: B a. In the figure, if AX = (3x + 1) cm, BX = 4x - 1 cm, AY = 4x + cm, YC= 5x-1 cm and x = 2, prove…

A: SOLUTION-

Q: Show that (t) =| 2 3t is the fundar

A: Given that,            y'=A(t)y                          ...(1) where                A(t)=-1t1-6t23t

Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

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Q: Prove that if A C R and t > 0, then |A| = |AN(-t,t)|+|AN (R\(-t,t))|-

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