H ome Work : IF U = {x :x €N ,10 2 x 2 1} A = {2,4,6} , B={1,3,9} , Find: ANB, AUB А -В B-A 2) U-(AUB), U-(ANB), (ANB)U(BNA) .... 3) AXB ВХА , A? , B? Bn A

Q: If u = 2i - 3j + k and v = i + j - k, then u x v is:   (2, 5, 3) (2, 5, -3) (2, 3, 5) (2, -3, -5)…

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Q: E (u, v) = (u – v², u² + 1, v²) |

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Q: Let u = (-1,3)and v = (1, -1), then proj,yu is:

A: Given, u=(-1, 3), and v=(1, -1),   then, projvu =

Q: U = (2,2,2) and v= ) (5, 4, 2 Th an Suppou se %3D ū t V = %3D 3 ū 13

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Q: separation method 6x U=Uxx u (o,t)=2 uく」t)=4 ucX, o)= 3X ut (x,o) =0

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Q: BCs: u(0, t) =u (I, t) = 0, t>0 ICs: u (x, 0) = ƒ(x), u,(x, 0) = 0,

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Q: 3. Find the value(s) of h such that b is a linear combination of and a3. -()-) -() --() ај, а2, 5 aj…

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Q: ôu ôu ôt ôx? u (0, 1) — и(1,1) - 0,1> 0, : 0 in (0,1) × (0,+∞), u(х,0) — и, (х),0 <x<1,

A: Given that the heat equation ∂u∂t-∂2u∂t2=0withu(0,t)=u(1,t)=0with ICu(x,0)=u0(x)

Q: Let u = (7 - 21, 2 + 5i). and v = (1 + i, -3 - 6i). Find a. u+ V b. 2iu c. u•v d. lull. and Ilv|I.…

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Q: U, +u, =0, 0<x<∞ 0<y<b ( u(0, y) = f(y), u(00, y) = 0 , , u(x,0) = 0 u(x,b) =0

A: Solving the partial differential equation by separation of variables.

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (1, −2, −3), v = (3, 1, 0)

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Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). -=D1 a(x, y) a(u,v)

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Q: i. Find proj,u and projų v u = (2, –2), v = (3,1)

A: Given,  u=(2,-2) ,  v=(3,1)    We have to find vector projection of v on u

Q: Find (a) u − v, (b) 2(u + 3v), and (c) 2v − u. u = (−7, 0, 0, 0, 9), v = (2, −3, −2, 3, 3)

A: a). b).

Q: Let u = (1, 2, 3), v = (2, 2, −1), and w = (4, 0, −4).Find z, where 3u − 4z = w.

A: u = (1, 2, 3)3u = (3×1, 3×2 , 3×3)3u = (3, 6, 9)v = (2, 2, -1)w = (4,0,-4)

Q: u,v,w ∈ R3 ; Prove that [ u *v, v*w, w*u] = [u,v,w]2

A: [u v w]=(u×w).[(v×w)×(w×u)] where u,v,w are vectors.

Q: Prove that Ix I - I y I ≤ I x - y I.

A: We have to prove that  x-y≤x-y We know, x+y≤x+y Then,  x=x-y+y⇒x=x-y+y≤x-y+y⇒x-y≤x-y

Q: 1 3 2 Let y = U2 and W = Span {u,,U2}. Complete parts (a) and (b). 3 --e- a. Let U = u, u2 . Compute…

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Q: a(u,v,w) 6. If x = - vw – wu, y = uvw, z = u³ + v³ + w³, find -uv a (x,y,z)'

A: X=-UV-vs-wu Y= uvw Z=u3+v3+w3

Q: ) IH U = (1,2,3, - - 0), A = (2,4,6 .20), B = (1,3,5 . - 19) Verify Demargans laws

A: Explanation of the solution is given below...

Q: Let u = (1, 2, 3) and v = (1, 2, -1). Find u- – u. v and v U - V = V - U =

A: Given u = (1,2,3) and v = (1,2,-1)

Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (1, 4), v = (2, 1)

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

Q: 10. Find the generalized Hukuhara difference u OgH v, where u = v = (1,3, 5). Does their Hukuhara…

A: Given -  u = (1, 2, 3)  v = (1, 3, 5) Generalized Hukuhara difference (gH difference) will be -

Q: Find r' (2), where r(t) = u(t) × v(t), with u(2) = (1, ,2, – 1), u' (2) = (3, ,0, 4) , and v(t) =…

A: Solution :-

Q: azu Q5) Find u such that ax2 with u(x,0) = 0.5x2, u(x, 10) = 0, u(0, y) = 0, = 0 %3D u(20, y) = 1…

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Q: OQ in which máB:mBC:mCÀ = 2:3:4 a) máB b) mBC c) mCÀ d) mZ1 (ZAQB) e) m22 (ZCQB) f) mZ3 (ZCQA) g)…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Let v1 = (1,1,2) v2= (-1, 2, -2) v3= (-2,-1,1). Write u = (6,7,2) as a linear combination of v1 v2…

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Q: Verify that ||v-w||^2=1 when ||v||=2, ||w||=1, and v*w=2

A: By the definition of inner product and norm we can derive the following formula : ‖u-v‖2=⟨u-v,u-v⟩…

Q: Compute u + vand u-4v. u= u+v= - 5 2 V = -3 3 (Simplify your answer.)

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Q: let u=(3,4), v=(2,-3) and w=(2,-2)  find (u*v)w

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Q: The distance between u = (15, 7, 4, 6) and v = (3, 2, 1, 4) is 82 182 V182 O 48

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Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=

A: Given that, u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v

Q: U₁ + Ux+Vx = 0, v₁ + UxVx = 0, u(x, 0) = u(x), v(x,0) = vo(x).

A: Given clear explanation below.

Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

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Q: Let u 7 and w compute -5 u + 9 v -4 w. %3D -5 u + 9 v -4 w Ouestion Help: M Message instructor O…

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Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (−1, 2, 1), v = (0, 1, 1)

A: Given  u = (-1,2,1) , v = (0,1,1)Find   (a) u+v      (b) 2v      (c) u-v      (d) 3u-2v

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (−1, −1, 1), v = (−1, 1, −1)

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Q: Find w such that 2u + v u 3w = 0. (0, 2, 7, 5), v = (-8, 4, -3, 1) 1 -- (-) W = 3 -

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Q: Find u + v u = and v =

A: Find u + v u = &lt;6, 1&gt; and v = &lt;1, 7&gt;

Q: IAsa matrx with 10 rows and 3 columns then what are the dimensons of U. D. and v' using the way we…

A: It is given that,A has order 10×3

Q: In writing v as a linear combination of u ,u, &u, ( if possible) given: y = (3,0, – 6) , u , = (1, –…

A: The given vectors,v=3,0,-6, u1=1,-1,2, u2=2,4,-2, u3=1,2,-4

Q: u, v, w ∈ R3 prove that (u * v, v * w, w * u) = (u, v, w)2

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Q: Let u = (1, 2, 3), v = (2, 2, –1), and w = (4, 3, -4). Find z, where 2u + v – w + 3z = 0. Z =

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Q: K=(0,20) ) Show (K,0,0) field. 12) Show (2,t,)(K,Ð ¸º) Hlint: : fi R ->K, fa)=e*]

A: As per our guidelines I am only solving 1st. For 2nd kindly resubmit the question mentioning 2nd.

Q: Let u = (1, 2, 3), v = (2, 2, -1), and w = (4, 3, –4). Find z, where 2u + v – w + 3z = 0. Z =

A: u=1,2,3v=2,2,-1w=4,3,-42u+v-w+3z=0

Q: Determine whether R3 = span(u, v, w) if

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Q: V Given that X - N (44, 25), find s, t, u and v   (a) P (X≤ s) = 0.9808   (b) P(X ≥ t) = 0.7704…

A: A continuous random variable X is said to follow Normal distribution with parameters μ and σ2 if its…

Q: 17

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Q: (b) P = V3t +6 . O u = 3t2 + 6, P = Vu I| = V32 + 6, P = vu U = Ou = 3t, P = \u² + 6 O u = 2 + 6, P…

A: Given that, P = 3t2+6 . Now, P can be written in terms of u with proper substitution.