Question 2. a) Is there a linear map T :V → W, where dim V = 3, dim W = 4, rank T = 2, and dim ker T = 2?

Q: Question 6. Let (X,7) be a topological space and A, BC X. Determine whether (A- B) CA -B or not.

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

Q: Question 7 Show that if C C RP is connected, then its closure C is also connected.

A:

Q: Question 7. Let (X,r) be a topological space and A, BCX, Determine whether A-B2A-B or not.

A:

Q: Question 3. Consider the topology r= {X,ø,{a},{a,c},{a,b,d}} X = (a,b,c,d). Let A= {a,d}, find A and…

A:

Q: Problem 2. Let X be a countable set and let s e X. Consider the particular point topology Tp on X,…

A:

Q: Let →a=⟨−2,0⟩ and →b=⟨−5,5⟩ Find the projection of →b→ onto →a (   ,   )???

A: Recall: Projection of b→ onto a→ , proja→b→=a→.b→a→.a→a→

Q: Question 32 Given the map RA-R defined by (x,y.z) = (0,0,x,0) then rank of f is: OA.O OB. 3 OC.4 O…

A:

Q: 6. If Z is the ocentroid of AWXY, WR = 87, SY = 39, and YT 48, find each missing measure. W a) WS =…

A:

Q: Exercise 2. Which of the following maps o : (a) $(r, y) = (x², r*, y) %3D

A: Please find the sol in next step, Shall we solve one question only as you have asked more than one…

Q: Prove that if V = W ⊕W⊥ and T is the projection on W along W⊥, then T = T∗. Hint: Recall that N(T) =…

A: V = W ⊕W⊥ and T is the projection on W along W⊥To show: T = T*Recall that N(T) = W⊥, R(T) = W

Q: Problem 6. Let (V, (, )) be an inner product space. Show that if T: V→ V, linear, satisfies ||T(r)||…

A:

Q: Question 3. Let u = (1, 1, 1) E R³ and denote U = span(u). Let W = {(x1, X2, 13) E R³ : ¤1+ x2 + x3…

A:

Q: . Let P be a point inside an acute angle with vertex A. Let PM and PN denote the perpendiculars from…

A: Consider the given information:

Q: THEOREM 4.4 (LINEAR TRANSLATION) Let Y= aX + b; then: My(0) = eb" My(a0).

A:

Q: QUESTION 3 Calculate OF.dr if F= and C is the triangle oriented counterclockwise with vertices at…

A: please see the next step for solution

Q: Question 4 . Let (X, d) be a metric space and let p(r, y) is complete if and only if (X, p) is…

A:

Q: In which of the following cases is the mapping x: R² → R³a patch? (а) x(и, v) — (и, uv, v). (c) x(и,…

A: A mapping defined from x : R3 to R2 is defined a patch if x maps U diffeomorphic ally onto x (U) As…

Q: Question 1. Are the following linear maps invertible? a) T: R³ → R³ defined by T(r, y, z) = (y, z,…

A:

Q: Question 3. Consider the topology 1={X,.{a),{a,c),{a,b,d}} X = (a, b,c,d). Let A = {a,d}, find A and…

A:

Q: Question 12 Given u=21+31 and V51+2), ting the projection of u onto v.

A:

Q: Question No. o6: Evaluate the where C is yectangle ahere vertices (o,0)> (x,0), (x.%), (0 , %).

A:

Q: State if the following statement is true or false. The map p4 p 3 defined by (xv,z,w)=( w,z x, x+ y)…

A: Solution is given as below:

Q: Question 1 Given the map R-R+ defined by f(x,y.z)= (0,0.1,0) then nullity of f is: O A. O O B. 3…

A:

Q: QUESTION 8 The set M= EN: X< with the usual metric is connected. O True O False

A: Since you have asked more than one question. So we will solve first one for you. If you want other…

Q: Show that the points D(0, 3), E(−2, 7), and F(2, 9) are the vertices of a right triangle. mDE  =…

A:

Q: • Problem 1. Let (V, (-|·)) be an inner product space. Show, for all v, w E V, that |(v\w)| <…

A:

Q: mplify ƒ (x, y, z, w) to the simplest form. The Karnaugh map can b

A: Answer:   f(x, y, z, w) = y'w' + yz'w

Q: Question 9 If u = (2 + i,1 + i,0) , then norm of u i.e, llull = v7. True False

A: given u=(2+i,1+i,0)

Q: Question 1. Let AcX. Show that t= {Uc X :ACU}U{ø} is a topology on X.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Question 9 Line 3 results from a valid application of Material Equivalence to lines 1 and 2. 1. (L…

A: Since you have posted a multiple question according to guildlines I will solve first question(Q9)…

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: • Problem 1. Let (V, (-|-)) be an inner product space. Show, for all v, w e V, that |(v\w)| <…

A:

Q: Question 4 . Let (X,d) be a metric space and let p(x, y)=+d(x, y) d(r,y) for all r, y € X. Show that…

A: complete metric space is a metric space in which every Cauchy sequence is convergent. In other…

Q: 4. What is the image of the half strips as shown on the figure, under the mapping z iz? Under the…

A:

Q: • Problem 3. Let a,b e R, with a < b. With B[a,b] as above, define ||f|l := sup{|f(s)| : 8 € [a, b]}…

A: Given ∥f∥∞=sup{f(s):s∈[a,b]}

Q: (5,1,2) V= (4,-3.1) is ON -bas in RB V to U Given Qud Find the projection W of Determine the engle a…

A:

Q: Question 1. Are the following linear maps invertible? a) T : R³ → R³ defined by T(r, y, z) = (y, z,…

A: A mapping is sid to be linear transformation if, (1) T(cx+y)=cT(x)+T(y) for x, y any vector and c be…

Q: Question 34: let 1R be the set of 1eal numbers and let ()SHow that the maping T:IRKG>1R. defined by…

A:

Q: Question 18 Which of the following maps is not linear? T.L.I.f:R3-R3 O a. T(x.y.z) = (1,0,0): Ob. f…

A:

Q: Question 13 Which of the following maps is not linear? O A T:R2→R2 defined by T(x,y) = (x²,x+y)* O…

A: Option A is not linear map because it does not satisfy linear property. All other satisfy linear…

Q: Find all maps ¢:(Z,+) → (Q*, ×) satisfying O (a + b) = ¢(a) × ¢(b) Va, b e Z

A: We derive the function from the given properties.

Q: QUESTION 5 The set R-{0} with the usual metric is connected.

A:

Q: find the projection of v onto u. Draw a sketch

A: Evaluate u·v,u·u and obtain the projection as shown below:…

Q: Problem 22. Prove that there does not exist a linear map T : R – R' such that range T = null T.

A: Rank nullity theorem: Define a linear transformation Given linear transformation is:

Q: Question 9 Given the map f:R4 3 defined by f(x,y,z,w) = (0,0,0)- Then nullity of is: → IR O A. 1- O…

A: Explanation of the answer is as follows

Q: Question. 2 Show that Span (x₁,x2,...,x,y) = Span (x₁,x2,...,xn) if and only if y is a linear…

A:

Q: Problem 1. Let (V, {-|·)) be an inner product space. Show, for all v, w e V, that |(v\w)| <…

A: Given: V,·|· is an inner product space.   To show: For all v,w∈V, v|w≤v|v12w|w12

Q: Exercise 4.1. Let F : R² → R² be the map defined by F (;) = () for any () E R². Describe the image…

A: Let ab∈R2 If ab satisfies x2+y2=1 then, 2a3b satisfies the equation x22+y32=1.

Q: Let a = (- 3, – 5) and b {1, 2). Find the projection of b onto a. proj; b = >

A:

Q: 1. Let T: R3 R3 be a linear image, which satisfies that (-3 Tei = -3/22, T(ez) = 9/2 and T (es) = -3…

A: