5) Let A and B be sets. Define the coordinate projection maps П1: Ах В А По : Ах В — В (а, b) у а (а, b) ь Let S C A. Prove that (S) = S × B.

Q: Let a = (5, 5, - 3) and b = ( – 5, 3, 0). Find the projection of b onto a. proj¡ b = <

A:

Q: Let C be the line segment joining A(1,1,1) to O (0,0,0). A parameterization

A: Given that A(1,1,1) and O(0,0,0) Find a parameterization

Q: The set of all directed line segments that are equivalent to a given directed line segment PQ\is…

A: The set of all directed line segments that are equivalent to a given directed line segment PQ \ is a…

Q: Let Q be the parallelogram in R2 whose vertices are (1, 1), (3, 2), (4, 5), (2, 4). Find the map T…

A: As per the question we first have to find the linear transformation T, whose inverse which will…

Q: Let u= and v= Show that is in Span (u, v} for all x and y.

A: Given u=4-1 , v=41 and b=xy. The vector b=xy is in span u,v if the system containing u,v and b is…

Q: Let (X,T) be a toplogical space, A, BC X. Show that АС В Ас в, АсВ. 介

A:

Q: Let v be represented by the directed line segment from (0, 0) to (3, 2), and let u be represented by…

A: Given that, v is a line segment from (0, 0) to (3, 2) So, v=(3,2) - (0,0)= (3,2)   Given that, u is…

Q: 2. Let A = {r|x is older than 25}, B = {y|y_is older than 50}, C = {z |z is between 20 and 30}. Draw…

A: The question is related to sets. The solution is explained below.

Q: given two sets X={-1,0,1} and Y={u,v,x,y,z}. There are 125 mappings from X to true or false

A:

Q: 1. Consider the finite projective Geometry satisfying the well-known axioms A1-A6 and having two…

A: GivenConsider the finite projectile.Geometry satisfyingthe well known axioms. A1-A6 and havingtwo…

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: Let C C R³ be the directed line segment from (1, 1, 1) to (3, 2,0). Evaluate

A:

Q: Let A = (2, 3, 5) and B= (x, y). Let p, and p, be the projections of Ax B onto the first and second…

A: Given that A={2,3,5} and B={x,y}. Let p1 and p2 be the projections of A×B onto the first and second…

Q: Let a = (– 5, 5, – 3) and b = (2, 1, 3). Find the projection of b onto a. proja

A: Projection b onto a is b→.a→a→2.a→

Q: Prove that if A-C-D, B-F-C, and A-F-G (all in the same plane) and A, B, and C are noncollinear, then…

A: Given:  ACD , BFC and AFG all are in same plane and A,B and C are noncollinear , then G is the…

Q: Use the Ruler axiom to prove that there is a one-to-one correspondence between any two lines.

A:

Q: Let a = (- 4, 5) and b = (4, – 3). Find the projection of b onto a.

A:

Q: Find c such that (4,−1),(−1,−8), and (c,−6) lie on a line. c=

A: We have to find the value of c such that the given three points will lie on a line.

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

Q: Let u = and v = Show that is in Span (u, v} for all x and y. y -1 5

A:

Q: Let ā = (– 1, 4) and b = (4, 5). Find the projection of b onto ä. proją b > Next Question

A: answer is in next step

Q: Prove: In Fano’s Geometry, show that for a set of three lines not all containing the same point,…

A: Axioms3 of Fano’s geometry: The axiom 3 in Fano’s geometry is stated as “not all points of the…

Q: Let U = {m,a,t,h,e,w,d,i,n} X = { e,w,m,a,t} y = {e,w,d,i,n} Z= {h,e,w}…

A:

Q: The point on the directed line segment from (2,0) to (14,12) that divides the segment in the ratio…

A: Topic:- geometry

Q: Let a = (– 3, – 1, 2) and b = (- 4, – 3, 2). Find the projection of b onto a. proj, b =

A: Use the projection formula for the given vector .

Q: 1 Let C = [c1, c2, c3] = -1 2 3 -1

A: Steps to find the projection of c1 : Find the orthonormal basis e1 of c2 and e1, e2 of {c2, c3}.…

Q: Let the set H be the union of the line segments from (1, 1) to (1,3), from (1, 2) to (2, 2), and…

A: Given that H be the union of the line segments from A1,1 to B1,3,from C1,2 to D2,2, and from D2,2 to…

Q: Let a = (4, 1) and b = (2, – 2). Find the projection of b onto a. proja

A: We have to find projection of b→ onto a→ for given vectors a→=4,1 and b→=2,-2 We know the projection…

Q: Let r = ⟨x, y, z⟩ and r0 = ⟨1, 1, 1⟩. Describe the set of all points (x, y, z) such that r − r0 =…

A: Given: r=x,y,z and r0=1,1,1 To describe the set of all points x,y,z such that r-r0=2 Solution:…

Q: Let C be the line segment joining M(-1,3,4) to O(0,0,0) and C' be the line segment joining O(0,0,0)…

A:

Q: By inspection, determine if each of the sets is linea (a) S= {(1, -2), (2, 3), (-2, 4)} O linearly…

A:

Q: Show whether the sets are connected or not. 1. {z € C | 1< ]z| < 2} 2. D(0, 1) U D(2i, }),

A: 1. Given: D⊂E⊂A then D=E    To Find: To whether the sets are connected.   Where z=x+iy           z…

Q: Let ā = (- 4, - 5) and b (- 5, 0). Find the projection of b onto ä. Round your answer to at least 3…

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: Let a = (- 4, 3, – 2) and b = (- 1, 2, – 3). Find the projection of b onto ä. proją b > V

A: Answer:Given a→=&lt;-4,3,-2&gt;b→=&lt;-1,2,-3&gt;projection b→ onto a→ is given…

Q: Prove or disprove that AS is congruent to SB (or that CS divides AB equally) if a line is drawn from…

A: Given, in △ABC, AB=AC=aBC=bBD=CDAD=h (altitude) To prove: CS does not divides AB in two equal parts.…

Q: Assume a directed acyclic graph is encoded as a relation R. Give a concise proposition stating that…

A:

Q: 6.1 let T: R?>R? be a linean frans formatien such that T(,,)> (4,0,-1), T(0,-1, 2) = (-4,2,-1), and…

A:

Q: Let a = (– 3, – 4) and 5 = (1, 2). Find the projection of b onto a. proja b

A:

Q: Suppose that {u, v} is a linearly independent set. Show that the set {u – v, u + v} is also linearly…

A:

Q: 2. Consider the directed line segment from M(2,7) to S(10, -4). Points A, R, and K are on MS. (30 27…

A: Given: Directed line segment from M(2,7) to S(10,-4). Points A,R and K are on MS.

Q: Suppose Ak,., A2 , A1 and B are points on R" Prove that if {A1 , A2, .. Ak} is an independent linear…

A: proof :- A1,A2,...Ak are linear independent set ⇒c1A1+c2A2,...ckAk=0  where c1=c2=...=ck=0…

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: Consider the map S: M2,2 → M22 defined by S(A) = AA.

A: Consider the map S(A): M2,2→M2,2ByS(A)=AATo check S(A) is linear transform.

Q: Suppose {p, p,, P3} is an affinely independent set in Rn and q is an arbitrary point in Rn. Show…

A: Here, {p1,p2,p3} is an affinely independent set. So, {p1,p2,p3} are linearly independent.

Q: Let ā = (4, – 1) and b = (– 2,0). Find the projection of 5 onto ā. proj, 5 %3D

A: Let a→=4,-1 and b→=-2,0 To find projection of b→ on a→

Q: Let a = (4, 0, – 5) and b = (- 2, 5, 2). Find the projection of b onto ä. proją b

A:

Q: Let the set 7 be the union of the line segments from (1, 1) to (1,3), from (1, 2) to (2, 2), and…

A: Givan that H is the union of line segment  H = { from (1,1) to (1,3), from (1,2) to (2,2), from…

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

A:

Q: e Guen an example to shus thet the inege lincarly independant set under a Lucar may mapping not be…

A: We have to give an example of a linear mapping which maps linearly independent set to linearly…