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Q: Consider the following inner product R?. on ((T1. Yı), (T2. Y2)) = ax122 + by,Y2 If ||(1, 3)||² =…

A: We will find out the required value of a+b.

Q: get an 6Usc Thesrmn to show that -x gra) = 2 has a unique haed %3D point on

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

Q: O Let ref(Al=Bmrz0 (2 20 X20 where dij = 10 for all i,5 - which is a True state ment? a) (A,Aay-,…

A: If a matrix is of reduced row-echelon form then it is an identity matrix with linearly independent…

Q: H.W. Classify the following eq.,and reduceit to the canonical form: (3)U+Uyy = 0

A: As per company norms, we are supposed to answer only first question in case of multiple questions.…

Q: 15. Verify the SSS Postulate for triangle congruence by using congruence transformations. Given: XY…

A: Given: XY¯≅RS¯,YZ¯≅ST¯,ZX¯≅TR¯ To prove: ∆XYZ≅∆RST

Q: Consider j1,ỹ2, ỹ,ER° and that ỹ,+y;+ÿ;=0. For Î=span{ÿ, ,ÿ and Y=span{ÿ2, ÿ}, show that Ý=Ỹ.

A: Given y1→, y2→, y3→∈ℝ5 such that y1→+y2→+y3→=0. Let Y^=spany1→,y2→ and Y~=spany2→,y3→. To show…

Q: a b (6) Identify all of the nonempty submatrices of A = с d

A: Given that:Matrix A = abcd

Q: Prove that K = {x+yv3 ] x, y E Z} is a subring of R.

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Q: (c) Show that the ideal generated by x² + y² + z² € C[x, y, z] is a prime ideal.

A: If <x2+y2+z2>is not a prime ideal, there should exist g,h∈ℝx, y, z s.t. x2+y2+z2 | gh,…

Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

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Q: Use the reflaction principle lio find the mumber of 2. paths a So =2 for Bimple randon malk from to…

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Q: 4. Let I and J be ideals of R. Prove that ifINJ={0}, then rs = 0 when reI and s eJ. %3D

A: Given that R be a Ring snd I.J be two ideals of R .Let r∈I and S∈ISince , r be an ideal and S∈J≤R…

Q: A) Show that the surtace x-2yz ty' =4 is orthogon al to any of the sm tamily of sur faces…

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Q: Con sider X={,2, --., 106? togcther with the largest 8-algebra p(X). capower set of x). Define 1 if…

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Q: Evaluate fr z sin(z2) dz where I is the union of the directed line segment that joins the origin to…

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Q: (2,4,2) √(122) Axlna +(By²2)] + (2 +9³) 2² what should A ond & be for the integral to be path…

A: Let us denote F1=Axlnz, F2=By2z and F3=x2z+y3. We have to find the value of A and B such that the…

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A: Consider a function f(x) such that:

Q: Let xe" and yer show that <xiy)=ytx is on imer product %3D

A: We have to show that &lt;x,y&gt; = y*x is an inner product

Q: 4. Show that the norm on (° given by I| (21, ..., In...) |lo= sup{|7;| : j =1,2, ...} %3D can not be…

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Q: 1. Given that z = x+ iy, where x, y are real and y #0, express z + 1 in the form a +bi where a and b…

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Q: Consider the following. u = −7i - 2j - 4k, V = 4j + 4k (a) Find the projection of u onto v.

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Q: Let z2T3-L p=S+Si O fird all the complex mumbers %3D guien by hza

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Q: Show that for any nontrivial ideal I of Z[i], Z[i]/I is finite.

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Q: c If in is an involution of X, show that (r, y)in = (yi", rin) is an involution of X12). %3D

A: Given X is a lattice. Given in  is an involution of X To show: x,yin=yin,xin is an involution of X2…

Q: Show that if, in using the Laplace development, you accidentally multiply the elements of one row by…

A: A 3×3 matrix a11a12a13a21a22a23a31a32a33.

Q: Prove that z'e'-z = 1 has exactly two roots inside the circle |z] = 1.

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Q: a T: Raz]M2x2(R) is given by T(a+ bx + ca?) = (, %3D b b+c-a, Which statement about Tis correct? O…

A: Given transformation is linear transformation, T:ℝ2x→M2×2ℝ s.t Ta+bx+cx2=acbb+c-a. Let,…

Q: Let C:z-1 in the counterclockwise direction and / = . Lnzdz, J = , zdz, and K = $. cotzdz. For which…

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

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Q: a, be R H I 's an ideal of R if and anly of a-beI. for then a+I b+I %3D

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Q: Q3. Show that p = 1– x + 3x? and q = 9x + 3x? product in are orthogonal with respect to the inner…

A: As per bartleby guidelines, for more than one question only 1st one is to be answered. Please upload…

Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: - If A is an ideal of R and x, y e R then prove that (i) x e A A+x=A (ii) A +x = A +y e x-ye A.

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Q: 1. Show that the definition (x1, x2) · (Y1, Y2) = x1Y2 is not an inner product on R?.

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Q: a b r s - Let R а, b, d 0 d r, s, tE Z, s and S even}.ir If S is an ideal of R, what can you say…

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Q: prove that the Lollowing examples satisly Laplace eqadion are -2y Cos 2X

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Q: If a translation maps zH onto LJ, which of the following statements is true?

A: First, we must perform the analysis of the diagram:   1. By translating angle H to angle J,…

Q: O8.D. If w, and w, are stri (x, X2) -(y Ya) = x,y,W,+Xay,W, uinlde an inner product on R'.…

A: 8.D  Let w1 and w2 are strictly positive i.e. w1,w2&gt;0.(x1,x2),(y1,y2)∈ℝ2Define the product…

Q: show that the. following Complex functron is dis continuous at z=i. fCZ) = スー! %3D 3.

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Q: let Z be aranelom vanimble with Pelf (Z~Nco) Show that , the psf of Z² (Y=Z) is. chi-square

A: # Given : z be the standard normal variate  let y=z^2  then to show that y follow chisquare…

Q: a) Suppose that you wish to prove that ARST = ASRV. Using the reason Identity, name one pair of…

A: Given: We wish to have the triangle RST and triangle RSV to be congruent.

Q: Show that 2Z U 3Z is not a subring of Z.

A: show that 2Z∪ 3Z is not a subrings of Z:   Solution:-             Let 2∈ 2Z∪3Z…

Q: 9) suppose that horx)=1, f,(x)=x ond dz(X) Prove that Ba(f, - where Ba is a Bernyterh Polymomial.

A: Given functions are f0(x)=1, f1(x)=x and f2(x)=x2 Since Bernstein polynomial is…

Q: Prove the following: 7. Given: PS bisects ZRST, 2SP = 3SQ, 2ST = 3SR T. Prove: ASTP~ASRQ

A: topic - similar triangles

Q: 3 use the definition of latlace transforms to find £{+²H (E-5) } JINO

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Q: Determine whether T={(a, -a) | a EZ} is a subring of ZxZ-

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Q: What are the perpendicular generators on (P) to 4 %3D of the surface

A: Given equation s are, x216-y24=z....1x3=y2=z-4...2 Equation of generators of the hyperboloid (1) are…

Q: (d) Prove Ker(f) = 1/J (e) Apply the Fundamental Homomorphism Theorem (FHT)

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.