3. Let (X, d) be a metric space and x1, x2, ... , Xn, ... a sequenc

Q: Let 2 v = w = and 0 = 3 Which of the following sets are linearly dependent? Select all that apply.…

A: Solution:Given vectors are      v→=203     ,  w→=111   ,  0→=000

Q: (b) How can you use vectors to determine whether four points in 3-space lie in the same plane? 2.

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Let →a=a→= and →b=b→=. Find kk so that →aa→ and →bb→ will be orthogonal (form a 90 degree angle).…

A: We Know that, Two vectors u and v are said to be orthogonal vectors if and only if u . v=0 Here, a =…

Q: 13. Find the intersection of [x, y, z)=[-8,-3,-5]+[1,2,-1] and [x. v.]=[1.9,4]+s[2,1,7].

A: We can find the intersection of the curve .

Q: How, Form P.D.E. from: a (3) Ucx,y) = (x²+a)lytb)

A:

Q: _et a₁ = -1 a₂= -7 -7 3 and b = 3 -15 h For what value(s) of his b in the plane spanned by a, and a

A: If b is in the plane spanned by a1 and a2 then b can be written as linear combination of  a1 and a2…

Q: 4. Let XRx R, where R is the set of reals and let d be the Euclidean metric on X. Show that the set…

A:

Q: Let u = 4 h = V= and w= 1 . For what value of h is w in the plane spanned by u am

A:

Q: Make r the subject Y=x-r/x+r

A: Y = (x-r)/(x+r)

Q: Let S be a set of five distinct points in the plane with integer coordinates. Show that the midpoint…

A: Given S to be set of five distinct points in the plane with integer coordinates. Let the coordinates…

Q: Find a plane containing the lines x = 3+ 21 x =1- 21 y = 4– 31 and y = 7+41 where -o <t<00, z =1-31.…

A:

Q: Question 3. If X and Y are isometric and X is complete, show that Y is complete.

A: Given below the detailed solution

Q: az Q.7 If z(x + y) = x2 + y?, show that lax = 4 ду. - +(1 - ax ду.

A:

Q: Q. (x,BCTR. pMl Barel space AnB = $ HCAUBUC)= ? MLAUBUC)= HCAUB)a M(BUc)

A: Measure

Q: Which among the following diagrams correspond to the metric below on the real plane R^2?…

A:

Q: (d) Passing through the point (0, 1, 2), perpendicular to the line L and intersects L. L(xo. v) =…

A:

Q: 3. Determine whether each of the properties is a topological or geometric prop- erty. Erplain your…

A: Given: Three properties are topological or geometric.

Q: If A and B are distinct points in 3-space then |AB| = - Select one: True False

A:

Q: 5- Determine the value for x such that the points A(-1,3,4),B(-2,3,-1), and c(-5,6,x) all line on a…

A:

Q: 6) Let f(z)=(2²-z-1)7. If a²+a+1=0 and Im(a)>0, then find f(a). a) 128a b) -128g c) 128g² d) -128g²…

A: Note: As per our policy, we are allowed to answer only first part of question kindly post remaining…

Q: Evaluate | xyzdx + In(xy)dy + xzdz over the straight line segment from (2, 1, 1) to (–1,1, –2)

A: We need to evaluate integral∫Cxyzdx+lnxydy+xzdz over the line segment from 2,1,1 to -1,1,-2.