If P and Q are represented by the numbers z1 and z2 such that H- then the circumcentre of AOPQ, (where |Z, Z, 1 1 1 1 z, z, O is the origin) is (A) 2 Z, - z, (В) Z, +Z, (C) 2 +z, (D) Zi + Z2

Q: Determine integers j, k, u and v so that the set S = {(j+kn, u + vn) : n E Z} is equal to the set T=…

A: Equation  157x+107y = 1 is a linear Diophantine equation (ax + by = c). Here , a = 157 b = 107 and c…

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A: We need to find the solution to the threshold problem in the next wave equation by the variable…

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Q: Prove that the four points P(2, ;1, 1), Q(1, 3, ; 2), R((2, 1, ; 3) and S(3, 2, 0) are coplanar

A: Given four points are  P(2,1,1)Q(1,3,2)R(2,1,3)S(3,2,0)

Q: Prove that if w=f(x, y, z), x=r-s, y=s-t, and z=t-r then dw dw dw + + = 0. dr ds ôt

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Q: If y is orthogonal to both and then y is orthogonal to every w in Span{u, v} V. O True False

A: We have to solve given problem:

Q: 3. AABC is isosceles with AB = AC; M and N are the midpoints of AB and AC respectively. If 41 = %3D…

A: Use the congruency property

Q: 1. Let A = (x1, Y1), B = (x2, Y2), and C = (x3, Y3) be distinct points on the plane. Show that the…

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Q: (c) If X= R, with r={ R, ¢, Q, Irr}. Show that (R, t) is a compact space.

A:

Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

Q: Let X and Y be two T, spaces, then X×Y. :is

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Q: Given sets X and Y. For x EX and for y E Y, we form the Cartesian produc X x Y := {(x, y) : x E X, y…

A: Given that: X={-1, 1}Y={-2, 0, 2}

Q: 2. Prove that there are no rectangles in S2. More precisely, prove that if A, B, C, D E S² form a…

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Q: Let A₁, A2, A3,..., A,, are n points in a plane whose co are (x₁, y₁), (x2, y2),..., (x, y),…

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Q: 5. If r = (r, (x, y, z) and ro = (xo, Yo, 20), describe precisely the set of all points (r, y, z)…

A: We plug the given values in the given equation and simplify

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A: Suppose there exist a homeomorphism f:[0, ∞)-----&gt;R then restriction of f f|[0,∞)\{0} : [0,…

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A:

Q: 4. Consider the space (R,T), where T={R,Ø}u{AcR:[0,1)cA}. If A=(0,1), then the closure of A is: * O…

A:

Q: Suppose n is an integer and z-z3D =r is a contour traversed n dz %3D once in counter clockwise, then…

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Q: Consider the sets X = {(x, y) E R²: x² + y² ≤ 1) and Y = ((x, y) = R²: x ≥ 0]. Sketch on R²the sets…

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Q: Let, T:R' → R';T(x,y,z) = (x + y+ z,2y+z,2y+3z) 2. Find the dimension of KerT and ImT

A:

Q: Let F = (z, 2x, y) and C is the straight segment from (0,0,0) to (1,2,3). Then ,F dř = %3D %3D

A: Given,                                   F→(x, y, z)=z, 2x, yand C is the straight segment from (0,…

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A: This is a question of point-set topology.

Q: 4. Consider the space (R,T), where T={R,Ø}u{AcR:[0,1)cA}. If A=(0,1), then the closure of A is:…

A: consider the space (IR,T)where, T = IR,ϕ∪A⊂IR[0,1]⊂AIf A = (0,1), then closure of A is

Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

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Q: an open ball in the set X, with its radius & satisfying -d(x, a), Vx € X at the open ball Be (x)…

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Q: Which of the following sets has oo in its interior: (a) {z = « + iy, x² 0} (c) {z = x + yi, |z +1|…

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Q: (2) Let P = (1, 1), Q = (4, –2) and R = (2,3). Find the point S such that R$ is equivalent to PQ.

A:

Q: 28. Bounded by the planes z = x, y = x, x + y = 2, and z

A: Solution:-

Q: 11. Let a, = 3 For what value(s) of h is b in the plane spanned h a =-8, b=-5 by a, and a2? %3D 2)

A: Given- a1=13-1 , a2=-5-82 , a3=3-5h To find value of h for which b in the plane is spanned by a1 and…

Q: 1. In R2, what is the dual cone V* if the primal cone V is V %3D {y1 (-3, -4) + у2 (1, -3) |у »3 0}

A: Given: V={y1(-3,4)+y2(1,-3)|y&gt;=0}

Q: Let P = {(z, y, 2) E R° | az + by + cz = 0} where (a, b, c) # (0,0,0). (a) Prove that (a, b, c) ¢ P.…

A: Given that P=x,y,z∈ℝ3 : ax+by+cz=0 where a,b,c≠0,0,0 (a) The objective is to prove that a,b,c∉P Let,…

Q: 1. In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) | y >= 0}

A: In R2, what is the dual cone V* if the primal cone V is V = {y1 (-3, -4) + y2 (1, -3) I y &gt;= 0}

Q: matrisinin özdeğerleri aşağıdakilerden hangisidir? o {,-3} po {0,1} 9o {2,-글} {2, –}} d) o {2, –2}…

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Q: (b) If the vertices of a polygon, in counterclockwise order, are (x,, y,), (x2, Yɔ), · .. (X area of…

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Q: 4. Consider the space (IR,T), where T={R,Ø}u{AcR:[0,1)cA}. If A=(0,1), then the closure of A is:…

A:

Q: Show that fi(r) = rª and f2(r) = r² +1 are orthogonal on the interval [–1, 1).

A:

Q: a let a bereal number . Explan why the planes x + 2yf az = || and ax + 2y +az =17 are uot orthogonal

A: if plane are orthogonal then cos x = 0

Q: 1. Let z, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

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Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

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Q: Prove that u, v, w ∈ R3     and [ u x v, v x w, w x u] = [ u, v, w]2

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Q: Let u = (1, 1), v = (3, -2), w = (4, 3), and y = ( map from R² -3, 4). Let L be a linear | to R?…

A: We know Let  Given

Q: A subset W of R° is given by = {(x,y, z) | 2x = y = 2z}. (i) Write down the distinct elements of W.

A:

Q: Find f and f, and evaluate each at the given point. y' f(x, y) = e*y, (In 4, 2) f,(x, y) = f,x, y) =…

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Q: Let f(x, y, z) = 2x(y+z), x uv, y = v w, and z = w. Find in terms of u, v, and uw.

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Q: theorem/ Letxis Hilbert Sface and T, SEBCK),26F then D Pracf %3D 3.

A:

Q: Theorem. A rectangle R with side lengths 1 and x, where x is irra- tional, cannot be “tiled" by…

A: Without using the concept of linear algebra you can proof this. Let length of rectangle= 1 Unit…