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

Q: ủ (u x) = 0 for all u, v in R.

A: We will prove whether this is true or false as following.

Q: 3. For f(x, y, z) where x = u – v, y = v – w, and z = w – u: - Compute - Show that of - af af and af…

A:

Q: 5. Prove that So*(y – 0)dydr =

A:

Q: 1- iz If z = x +iy and w =- z-i show that w = 1= zis purely real

A: Use modulus property

Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express zx andzy in terms of fu , fy , and the…

A: Given, Let z=f(u,Y) u=ax+byY=ax-by

Q: Evaluate | Vtan a sec" zdx. O a. 2 z tani z +tani +C 2 O b. 2 tani æ + tan +C 2 Ос. 2 O c. 2 2 t…

A: To evaluate the integral,  ∫tanxsec4xdx Rewrite the term sec4x=sec2x·sec2x…

Q: Prove Theorem (A + B )T = AT + B T

A: Prove Theorem (A + B )T = AT + B T

Q: 2. Show that by using MEAN VALUE THEOREM. u-v n >0 1+v2 3 <tan- < and deduce that 25 ww 4

A: First we have to show that v-u1+v2&lt;tan-1v-tan-1u&lt;v-u1+u2 where 0&lt;u&lt;v. Then we will show…

Q: Let x, y ∈ R. Suppose x^2 +y^2 = 0. Prove that x = 0 and y = 0.

A:

Q: Q2. (e) Verify that the Cauchy-Schwarz inequality holds. įu=(-3,1,0), v=(2,-1,3) u u=(0,2,2,1),…

A:

Q: Show f(x) = e and g(x) = xe linearly independent by finding its Wronskian.

A: Given: fx=exgx=xex The formula to obtain the Wronskian is Wx=f(x)g(x)f'(x)g'(x), where f(x) and g(x)…

Q: Prove by mathematical induction: X n (U-, Y) = U=1(X nY), for V n E Z* – {1} and sets X,Y,,Y2,. Yp-…

A:

Q: In rank - sign test, the null hypothesis u = µo can be rejectedin favor of %3D the alternative u < u…

A: Signed rank test HypothesisHo:μ=μ¯oHo:μ&lt;μ¯oWe reject the null hypothesis if W+≤Wαwe reject  the…

Q: Use Fermat's Theorem in your proof that Vn E Z>², 2 is irrational. I

A:

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

A:

Q: Show that: (a) Cov(X,Y) = E[XY] – E[X]E[Y]. (b) If X and Y are independent, then fY|X(y|x) = fY(y)

A: Solution:a.Show that COV(X,Y)=E(XY)–E(X)E(Y)

Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express z x and zy in terms of fu , f y, and the…

A:

Q: Prove that (V + w)× (v – w) = 2(w x v). |

A:

Q: defined BCX,x). a norm Dn

A:

Q: y Verify Euler's theorem for u = x' In

A:

Q: find the values of c that satisfy Rolle's Theorem

A:

Q: Show that the functions e*, cos x, and sin x are linearly independent using the Wronskian.

A:

Q: Where x = (X1, X2) E R². 3- N: R2 - → R defined by N(x) = /x1² + x2² is a norm on R². (x1, x2) E R².…

A: Let X=(x1,X2)€R^2

Q: Prove that f, uv v • dỉ = – §̟ vũu • dĩ

A: Whenever the force is conservative in nature the work done over the closed loop is always zero. i.e…

Q: A function f(x,y) is homogeneous of degree 7 in x and y if and only if, __________.

A: Given problem is solved below.

Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: дz (B)If Z = f(x, y), x = s² - t², y = 2st. Prove that s მა 2 (s² + t²) of af əx I t дz at II

A:

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

A: Given : fx,y,z = x3-yz2

Q: X = R² and = = { $₁x} V { \\x>0} where U4 = {(x,y) | x² + y² <²} Prove (x, t) is Topology

A:

Q: Let x, y ∈ R. Suppose x2 + y2 = 0. Prove that x = 0 and y = 0.

A:

Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: Q2. (e) Verify that the Cauchy-Schwarz inequality holds. įu=(-3,1,0), v=(2,-1,3) uu=(0,2,2,1),…

A: Cauchy-Schwarz inequality relates the inner product of two vectors and their norms.

Q: 2-Express each function in the form u(x, y) + iv(x, y), where u and v are real, (c) ez2 (d) In(1+…

A: We have to write in u(x,y) and v(x,y) form.

Q: дz (B)If Z = f(x, y), x= s² - t², y = 2st. Prove that s მs 2 (s² + t²) of əx

A:

Q: 3. Prove F (Vr)(A→ B) → (Vx)A → (Vx)B. ->

A:

Q: Find all the joint moments m,1, n and k= 0, 1. . .

A:

Q: Let u(x) be a solution of u" – q(x)u = 0 with q(x) > 0 such that u(0) and u'(0) are positive. Show…

A:

Q: dv Prove that 4u/2n

A: We use Gamma function to prove the given result.

Q: prove using soundness that the converse of Axiom 2: (vx)A → A[x := t] is not a theorem

A: Solution: If Î" ` Ï• then Î" |= Ï•. Completeness If Î" |= Ï• then Î" ` Ï•. Thus, any formula proved…

Q: (a) Prove that if f e C (R²) then a (af af %3D

A: This is a problem of the calculus of several variables, higher dimensional calculus.

Q: Show that e", sin x, cos a are linearly independent using Wronskian Method.

A:

Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: on vectors for t2 0.

A:

Q: Compute the value of f.dr If F= -yi+xj and c is a from (-1,1Y to CI,1) %3D SemICirele

A: Proceed as shown below

Q: a- if w = f(u, v), u = x + y, v = x-y Prove that = ( - )* aw aw %3D ду du.

A:

Q: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.