f If Xo's Compact, x=y Continuous bijective L Topelagied space Then f is homeomorphism
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- Find unitary oxthogonal to Mlowing diagonalizeny an or matr'y tor One 2 0 0 (as (b) 3 -2 - 23C Given the Euclidean inner product space (R³(R),+,,*), where for each_x=(X₁,X2,X3), y=(yı,y2,y³)=R³, x*y = 2(x¹y₁+x³y3) + X2(Y1+Y3) + (x1+x3)y2 + 3x2y2. Show that matrix [2 1 01 A = 1 3 1 LO 1 2 is invertible and calculate matrix A-¹ using the Cayley-Hamilton theorem.let fec[a,b] and oejex be two real oummbass. осус have we 2 Σ fem) = [ f(ta+ + fit-Lets) filtrat ecto y (x-[x]) f(x) + (y-Ly]) fig). xsush Prove result R
- 3A Given the Euclidean inner product space (R³(R),+,,*), where for each_x=(X1,X2,X3), y=(yı,y2,y3) ER³, x*y = 2(x₁y1+x3y3) + X2(Y₁+Y3) + (x1+x3)y2 + 3x2y2. Check whether the matrix A of the inner product (*) is squared with respect to the natural basis of R³, without computing its eigenvalues and eigenvectors.Please try to give type solution fast i will rate for sure2b) Let ( X, T) be topdogical space and A,B C X- ldentify the Condition when a (Int(A)u Fr(B))Ul F CA) UInt (B)) and FRCA) UInt (B (CILA)N Fr (B)) U ( Fr(A) ncI (B)) are Same .
- Prove disprove that (R,T co-finite) is Te-space orAmetric space (x,d) is complete i fundonly ifx has the cantor intersection property3 brio NoM Prove that any complex c'nner product com plex veclor space v, there s on a basi's u. Un? so Un} That aSurface of a sphere is a two-dimensional Riemannian space. Compute the Chrtstoffel symbols.part v(a) Let M R. Give the radius r and the center c of B(-2,5) n B(6, 7). (b) Let M = R. Using interval notations, give a simplified expression for the set L= [B(1,1) UB(5,1)] n B(3,2). (c) Let = 3(-1)" + and A = {,: ne N). Give the set W of accumulation points of A. (d) Let A₁-(-2n, 2n) and K = U An. Give a simplified expression for the interior Kº of K. NEN (e) Give the set T of isolated points of B(0, 1) U (3) U (2,5,7) (f) Let [P,Q] be a segment in R2 with midpoint H, and let (1,0) and (2, 1) be the components of the points P and H, respectively. Give the components (x, y) of the point Q. (g) Suppose that f: (M, d) →R satisfies d(f(x), f(y)) - vl. Let 21 e M and set n+1 = f(n), for n e N". Assume that M is complete and let a = lim zn. Give a simple formula satisfied by a.SEE MORE QUESTIONS