7) Assume dim V = n, dim U = k, dim W = n - k, and U + W = V. Prove that Un W = {0} and V = U OW.

Q: 10 of 17 If y(t)+(t-r)y(r)dr=t, then y(t)= Su-nyndr3Dt,

A: Convolution Theorem: The Laplace Transform of the convolution of f(t) and g(t) is:…

Q: Show that a fomws with R>o Ssee igue] may be descuibed panometuicaly by u cU,N] Cosu, (R+ o…

A:

Q: ). Show that V - u -ly- tan' u < V - u 1- if 0<u<v, < tan 1+v? 1+u 4 2< tan 4 25 3 and deduce that 3…

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Q: 18, then Ku = 3 and µ4 Af U2 %3D %3D Select one: O Platy O symmetric O Lepto O Meso

A: Solution-: Given: We find

Q: 3. Prove that sinOtcos=1.

A:

Q: Verify that He follow egunbin is an ielartiky Fan o -sino 2 tano

A: We will use various trigonometric formulas to answer this

Q: 7. Show for y = u.v that y"= uv"' + 3u' v'" + 3u" v' + u''' v.

A: The detailed solution is as follows below:

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: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: 3) Use Green's Theorem to evaluate o-ydx+xydy where C is the line segment from (-2,0) to (2,0) then…

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Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

A:

Q: What is u × w, assuming that w × u = 〈2, 2, 1〉?

A: Given,w×u=2,2,1 To find:u×w Solution: We know ,by property of cross product of two vectors (say,a…

Q: 8. Chords AC and DE intersect at Point R in OQ. If AR = 6, RC = 7, and DR = 3, what is RE? %3D %3D

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Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

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Q: 2), Compute SE. di where Fュく-,) C is s shown

A: The general form of a vector valued function in three dimensions is given by F→=F1,F2, where F1 and…

Q: find the length of the SPIYAIV-e'sVom 0=0 to 0=V5

A:

Q: 8. Show that, for u, v E R³, ||u|| ||| = (u - v)² + ||u x v||².

A:

Q: Show that if Y = ax + b (a = 0), then Corr(X, Y) = +1 or -1. We know Cov(X, Y) = Cov x, ])--)-I + b…

A: We need to show that, If Y=aX+b then Corr(X,Y)= +1 or -1

Q: 9. Let u AB and v = =PQ where A=(-4, 6), B = (3, 3), P = (4, 5) and Q = (-3, 8). Can you verify that…

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

Q: =8, d=9 ation u such that (a, b, c, d) = p

A: The value of a, b, c and d are given as follows, a=5, b=13,c=8,d=9. To find the permutation μ, such…

Q: 1. What congruence postulate/theorem cannot be used to prove that ALIV AJIN given that LVis parallel…

A: topic- congruent triangles

Q: 20. Let -(). -- (). (). u = w = If au + yv = w. (x, y E R), then a - y = (A) 2/3 (В) —3/2 (C) 3/2…

A: To find  The value of x-y

Q: 9. Write a 2-column proof: Given: p // q , Zg = (59 + 5x)° , %3D Za = (11x – 7)° Prove: Za = 114°…

A: Explanation of the answer is as follows

Q: 3. Show that S, has the presentation (x, ylx* = y? (xy) %3D %3D

A: Given: Group S4 We need to show that S4 has representationx,y|x4=y2=xy3=1

Q: In R', the point (1, 1, 1) does not belong to the cylinder x + y = 2. Select one: True O False

A: Given problem:- In R³, the point (1, 1, 1) does not belong to the cylinder x² + y² = 2.  True  False

Q: Show that is Reciz) e -ImZ p (ii) Im(iz) = Relz). %3D

A: Solution:- we have to show that  (1)    Re(iZ) = - ImZ (2)    Im(iZ) = Re(Z) where , Z = x + iy

Q: Find and when (TU – V)² In(W – UV) = In(2) at the point (T, U, V, W) = (1, 1, 2, 4).

A:

Q: show by of R then IUI is not ideal example if In and Iz are icdeals an

A:

Q: If u, v are given unequal numbers anu (un-1+ Pn-1), vn = V (u –1 Vn-1), where n2 2 , %3D Un %3D 2…

A: Given

Q: prove that dv v 21/12 الله duz 2 2

A:

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

A:

Q: cos (o,+ O>)+ ì s:in (8,+Ə.)) Prove this kW- Mon 183O

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Q: Find first and second fundamenta! Texm U-V e Cos 2sin U-V of

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Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: Ju 20²u c² of2 (r, t) = u(x,0) = 0, ut(x,0) = 0 u(0,t) = 0 u(1,t) = 0. da2(x, t) + XX , 00,

A: Introduction: The basic method to solve a partial differential equation is the method of separation…

Q: 2 la), Pu (aw by Re currence relation

A: We have to find out P2(x) and P4(x) by recurrence relation. We know that the generating function…

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

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Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability

A: Use the deduction theorem: Deduction theorem states that, If ┌ A⊦B then ┌⊦ A→B

Q: and are 2 soihions and w Cy,,Y2)(to)to what con conclude ? we

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Q: Show that U. AS cuhere N= {3 unaluralnun %3D

A: To proveG={N,*} is not a group under binary operation a*b=ab where a,b∈N

Q: SR ⊥ RT, TU ⊥ US , ∠STR ≅ ∠TS PROVE: ∆TRS ≅ ∆SUT

A: Since SR⊥RT So, ∠TRS=90° Also as TU⊥US So, ∠SUT=90° ∠STR≅∠TSU (given)

Q: Determine las primeras derivadas parciales de la función en el punto (1,2) (u, v) = z*y - 3yA O(1,2)…

A: Find the first partial derivatives of the function at the point (1,2) f(x,y) = x2y-3y4

Q: If both z + w and zw are real, how to prove that either z = w (conjugate) or Im(z) = Im(w) = 0?

A:

Q: (a) Prove that x, y = -1, y = 1 1 (b) Prove tha and n: m and

A: This is a problem of Number Theory.

Q: In AJKL, JL is extended through point L to point M, MZLJK = (x + 9)°, mZJKL = (x - 2)°, and m/KLM =…

A: The exterior angle is equal to sum of two opposite interior angles. We will use this property to…

Q: Suppose that fo sf,:X-gy and g,-3 YoZ Prove that (Hint : First use ce) to show that gfe g,, and then…

A:

Q: Compute / (1/zy, 1/(z + y)) dr along the path from (1, 1) to (3, 1) to (3, 6) using straight line…

A: The parametric vector form of a straight line from (1,1) to (3,1) will be given by:…