A prove that Newboń's for ward formal?

Q: 8.0. If x-(x,, X, ...,%)«R', define [xL by Prove that xJkL is a norm on R'. N I|} dns - x]

A: We will solve the first question highlighted in yellow. If you want the second question to be…

Q: Compute det (A) using the cofactor expansion along the first column.

A: First we expand using the first column

Q: Prove that det(kA) = kn det(A) for any A ϵ Mnxn(F ).

A:

Q: 3.) Prove (cA)" = cCA) %3D

A: Let A be a m×n matrix so A=(aij)  1≤i≤m and 1≤j≤n ie A has m rows and n columns. By AT we mean…

Q: Find diagonal matriy D is similar with A a A = [3 8-5

A:

Q: - Show that the norm tion t= aT+B. Use [a, b] onto [0, 1] (7) = 1, ý(7)= T, V т,

A:

Q: 1. Prove by Induction that the numbr f edges of Kn

A:

Q: Prove that I(e) = dr, e> 0.

A:

Q: prove that 2. catX+c

A: We use that- sin2x + cos2x =1  so that 1-cos2x= sin2x

Q: Compute the orthaganal piojectian of ? onto the lina L through -6 and the origin

A:

Q: Prove the following version of Darboux's Th

A: To prove the Darboux's theorem:

Q: Prove that the set S = {n² : n e N} is denumerable. %3D

A: We have to show that the given set S is a denumerable set.

Q: Prove that on average, permutations of length n have H, cycles, where Hn i=1

A:

Q: Prove az - ae that d az dz

A:

Q: Find the infimum and supremum of the set X = {3 – Vztn ine N}. -

A:

Q: prove that the covariant derivate satisfies leibniz's rule

A: The main reason behind the covariant derivative satisfying Leibniz's rule is it maintains chain rule…

Q: Prove %3D 11

A:

Q: Orthonormalize the set {(¿).(9)} with respect to the inner product from before.

A:

Q: If n > 2, prove that Q„ has at least n!/2 Hamiltonian cycles.

A:

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: Hew.b prove that CAXB)-Ais atways-Zero

A: Topic:- vector  algebra

Q: Prove that Z(Sn) = {e} for n ≥ 3.

A:

Q: az Find if yz – In z = x + y ax

A:

Q: Prove that on average, permutations of length n have H, cycles, where Σ Hn i=1

A: We will take an arbitrary set containing n elements and observe the required permutations.

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

A:

Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

A:

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: Verify Eular,s theorem for z =ax2+2hxy+by2

A:

Q: Show that R³ is spanned by S = {(1,1,1), (1, – 1, 0), (0, 1, – 1)}.

A:

Q: Let gilx) i for n z2 i define gncr) -gn1(g,(), = 2ー× Deter mine the Intervai Such that g2avu CA) is…

A:

Q: If X is a finite dimension that an inner product o Yjk = (e, ex). Can we cho fashion? %3D

A:

Q: Prove that K4 is not outerplanar

A: In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices…

Q: let z- 5 dy By chain Ruie

A: Given z = √x dy/dx = (1/2√x)•(dy/dz) We have to find d2y/dx2 .

Q: IRI- 2. <| sinz|< -e 2

A:

Q: we need to find for and poove foinmmulas and This question is based on Secosd and umbers. of…

A:

Q: Let (X, F) be a о — algebra o - , and be two probability measures on (X, F) so that both are ergodic…

A: Let (X,ℱ) be a σ-algebra and μ≠v be a two probability measure on (X,ℱ) So that both are ergodic for…

Q: with the p-norm 「さい Is a normed lineur s pace over fiéle cary R with respect to opera tróns addition…

A:

Q: (a) Prove the following property: (:) - (.".)

A: Hey, since there are more than two questions posted, we will answer the first question. If you want…

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

A:

Q: prove that Sa/Gn has f discription with M-ly ny-l Degrees tof freedom

A: Suppose that xi and yi are two random samples of size n, drawn from a normal population.  Population…

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: Prove the following: %3D

A:

Q: 2

A:

Q: Show that R3 is spanned by S = {(1,1,1), (1, –1,0), (0, 1, – 1)}

A:

Q: what expressi on is equivaient to this. (n-a)!

A: n!(n-2)!+n=n×(n-1)×(n-2)!(n-2)!+n  [we use the idea of factorial]=n(n-1)+n=n2-n+n  [distribute n]=n2

Q: To test this null hypothesis, we compute t using a special case of the formula. state the formula?

A: In this case, we need to write the test statistic formula for testing the null hypothesis.

Q: Prove: |I| = 1. %3D

A:

Q: 3. Prove that the sandwitch theorem.

A:

Q: If e-ispure imaginary W hat Restriction is placed on z?

A: