3 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 a

Q: A set W is defined as consisting of all the planes in R^3 that are parallel to the plane x+2y-3z=1.…

A: A set W is defined as consisting of all the planes in R3 that are parallel to the plane x+2y-3z=1.…

Q: Each point of the parallelogram is translated up 3 units and left 2 units and then connected to form…

A: After shifting parallelogram 3 units up and 2 units left the new parallelogram will be

Q: e) Calculate the space generated by specify its base and dimension <-{()信)( 2.

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Q: Find basis for The Sspace for the of function that Satisty り

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Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: Show that D^2 = {(x, y) ∈ E^2: x^2+y^2 ≤ 1} ⊂ E^2 and the space containing a single point are…

A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: 3-) Find the pointls) to point Az(d,0) on x-3~y2 that are closest メ=2 25 +1,5 0.5 + - -ロ5 + 8.5 to…

A: here we have to find the point on the curve x=3-y2 that are closest to point A(1,0) let point is…

Q: Prove that the only idempotent elements in an integral domain R with unity are 0 and 1.

A: Idempotent element : An element a in a ring R is said to be an idempotent element if a.a = a .…

Q: ) Every continuous map RP2 → S² is homotopic to the constant map.

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Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

Q: Find foF dr where C is a circle of radius 3 in the plane x+y+z= 8, centered at (1, 3, 4) and…

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Q: show that L^1(R) a Banach algebra Commutative

A: We will define the multiplicative operation of Banach algebra in case of L1(R) and prove its…

Q: Use Clairaut's theorem to draw the geodesics of the catenoid

A: Solution :-

Q: Shoe that Hhe p qiuen by norm on (on ho f be given by a scalar prodluct

A: We need to show that the norm on l∞ given by: x1,x2,…,xn,…∞=supxj: j=1,2,3,… can not be given by a…

Q: Let R is ring of real numbers and *, (2) O defind on R^2 as follows, (a, b), (c, d)ER^2 then (a, b)*…

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Q: If N is a sphere of radius R that is centered around the origin. Use appropriate functions and…

A: Simplify the integral:  ∫Ωr→r3∇→r4-R4r5+7r3+2dτ=∫Ωrr3r^r^ddrr4-R4r5+7r3+2r2sinθdrdθdϕ…

Q: -}]-=[}]»=[}- [] 3 Find Let vị = and p = 3 a hyperplane [f: d] (in this case, a line) that strictly…

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Q: Show why the product {[x1, x2], [yı, y2]} = xıy2 does not satisfy the conditions for an inner…

A: See the detailed solution below.

Q: Show that at a hyperboic poin, he principall direcions bisect the asymptotic directions using The…

A: Summary:At a hyperbolic point on a surface, the Gaussian curvature is negative, indicating that the…

Q: det R have the inner Euclidian fipace product 4=(5,-1) and let X= L1,1) and Find l lyll and Kxy>…

A: Given that x=(1,1) and y=(5,-1)

Q: Classification of Second-order kartiat Differen tial Elations theorem: Let 2(x-S) = $(St), Where…

A: Given PDE is a∂2z∂x2+2b∂2z∂x∂y+c∂2z∂y2+φx,y,z,∂z∂x,∂z∂y=0                       (1) Here, we have to…

Q: Let M⊂R ^ 3 be a surface and f be a diff.bilir function on this surface. Show that if Q is this…

A: Given: Let M⊂R3be a surface and let f be a differentiable function on this surface. If Q is a 1-1…

Q: Consider the infinite geometry R^2, where points are (x, y) ∈R and lines are ax + by + c = 0 with a,…

A: We have to show that R^2 is an Affine plane.

Q: A) Show that the function u(x; y) = 5x4y - 10 x²y³ + y5 is harmonic and determine the harmonic…

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Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: IF en Inner pYoduct Space X iS Vea show thet condition Hnll=Hyll impLies +ye X-y>0c what does this…

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Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: Sr²e="dr

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Q: formela for the fun thn yoga) Con súto of two line 2) Write cmula whose as in fguve the f Mawing : 6…

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Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

Q: 2+9z X =,26+,A

A: Draw the quadratic surface y2+9z2=x using traces. Solution: The traces of the surface y2+9z2=x is…

Q: find alea in bounded and in which Juadiantgon メ-exis lies fist lind Give U-n. where is explession…

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Q: show that a=(2x^2+8xy^2z)i+(3x^3y-3xy)j-(4y^2z^2+2x^3z)k is not a solenoidal but b=(xyz^2.A) is…

A: Given:A=2x2+8xy2zi+3x3y-3xyj-4y2z2+2x3zk To check solenoid we will check ∇.A=0 or not…

Q: 3 Divergence the oven SS F. da S = = y*² 2 + (xy^² - 32¹) ŷ ? ^ use evaluate + + (x² + y²) 52) 3 and…

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Q: '99 '37 37 XCOS Z Evaluate dzdydx. and the sphere

A: