Express w as a linear combination of u and v. 4 --}-}--[:] W = 6 u 3 2 6 6

Q: Suppose u =(4,-5, 3). Then (-1,1,5) makes ? (4, 5, -4) makes ? (3, -3,5) makes ? (-6,0, 8) makes?…

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Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

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Q: verify that A(B + C) = AB + AC

A: Now,

Q: Suppose Duf(xo, Yo) exists. Show that Duf(xo, yo) = - Duf(xo, yo).

A:

Q: In(u)

A: We are asked to integrate the given

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: * Find the Cartesion Coordinates of the points. (),(万,). (-2,2)

A: To convert Polar coordinates r, θ to Cartesian coordinates x, y apply:x=rcosθ   y=rsinθ

Q: , x); R = [0, -) D) D = (-, x); R = [-10, -)

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Q: Consider f(x) =

A: We find out the critical point of given function putting f'(x)=0.

Q: 5(u-) du 2. 2

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Q: Let x = (3,-1,0) and y = (0,1,5). a) Show that no choice of numbers a and b can make ax + by =…

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Q: Find the distance between (9,23) and (-5,80) Show work

A: I have appended the formula used in the solution part of the question

Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

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Q: E. On the right: a. r*ak + r*(-ak) = r*(ak + (-ak)) b. r*(ak + (-ak)) = r*0 c. r*0 = 0 F. So, r*(aj…

A: the last three lines also proves b and c too.

Q: verify that (A + B) + C = A + (B + C)

A: Now,

Q: If u=(2,4)�=(2,4)  and v=(3,−4)�=(3,−4)  then proju(v)≈

A: The objective of this question is to find the projection of vector v onto vector u. The projection…

Q: 3,10 on coordinate plane

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Q: 2 1 -1 1-1 2 If A = 1 -2 3 B = -2 1 3 show that -2 1 2 2 -1 1 (A +B) = A? + AB + BA + B²

A: Given,           A=21-11-23-212 , B=1-12-2132-11

Q: If X ~ U(3,7), then P(X = 4) ≠ P(X = 7) true or false

A: X~U3,7

Q: Write the forward difference and backward difference for Uy

A: Forward difference formula:  The forward difference of yn is given by ∆yn = yn+1-yn. Backward…

Q: 10 8- A 6- 2 -10-86 246 8 10 B -8 MathBits.com -10

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Q: HO Let A = 1 -21 4 and B = 3 2 3 5-6 -1

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Q: 5. For which value of x do the following vectors form a linearly dependent set in ¹ X₂ G

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Q: Show that (z3 z4) -1 = (z3-1. z4-1)

A: We prove the given statement by taking Z3=x3+iy3, and Z4=x4+iy4. After using the fact of…

Q: Find the angle between u and v. - [8] -- [14] = B = U =

A: Given query is find the angle between the vectors.

Q: If ~v = 〈 4, 1, 6〉 and ~w = 〈3, 2, 3〉, find ~v · ~w and ~v × ~w.

A: If ~v = 〈 4, 1, 6〉 and ~w = 〈3, 2, 3〉, find ~v · ~w and ~v × ~w.

Q: 51 3 -[---] -4 2 -2 Let u= (a) 5u-2v, 3 V= 5 W= -1 Find:

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Q: Let a, b and c be positive numbers such that a ^ 2 + b ^ 2 = c ^ 2 Show that a + b> c.

A: Let a, b and c be positive numbers such that a ^ 2 + b ^ 2 = c ^ 2To Show:-  a + b> c.

Q: 2-) Gradient (2xy+3x²)e% + cx?2y242y)g-ce&) is fGriy,2) find the function.

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Q: Suppose u = (4, 3, 0), v = (−1, −5, 5) and w=(5,-4, 0). Then: ú.v= u.w= v • w=

A: According to the Bartleby guidelines we are suppopsed to do the first three subparts of multiple…

Q: Gven CA CE.BA a DE Prover BE DA

A: