Answered: Suppose {p, p,, P3} is an affinely…

Suppose {p, p,, P3} is an affinely independent set in Rn and q is an arbitrary point in Rn. Show that the translated set {Pi + q, P2 + q, P3 + q} is also affinely independent.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.7: Distinguishable Permutations And Combinations

Problem 15E

See similar textbooks

Related questions

Q: A set of ordered pairs in which each member of the set of first components corresponds to exactly…

A: A set of ordered pairs in which each member of the set of first components corresponds to exactly…

Q: Show that the set S = {(1, 2, 3), (0, 1, 2), (−2, 0, 1)} spans R3.

Q: Construct the intersection graph of the following collection of sets: 4 = {0,+2, 14, 16, ±,..} A, =…

Q: Suppose that A is a Hintikka set. Then, for all terms s and t, s = t E A or ¬(s = t) E A

A: Given, Suppose that is a Hintikka set. Then, for all terms S and t,

Q: Give an example of each of the following (a) a set which is a nbd. of each of its points, (b) a…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 9}. (Enter your answers as a…

A: First we write U and the set in roaster form.

Q: True or false? For all sets A and B, (A∪B)'=A'∪B' This can be determined by constructing a…

Q: For the set A= [-0, 4) U{5,9} U[6,7] , 6 is interior point of A ylgn İhi

A: False

Q: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

Q: the collection of all close subsets of R is called the topology of R

A: To check: Whether the statement is true or false: Given: The statement is "The collection of all…

Q: Give an example of each of the following : (a) a set which is a nbd. of each of its points, (b) a…

Q: If C1, C2 are connected subsets of R, then the product C, xC, is a connected subset of R?,

Q: Define the sets A, B, C, D, and E as follows: • A = {x €R:x 2} ' = {x € R: |x| < 2} • C = Do the…

A: A = x∈IR : x<-2B = x∈IR : x>2C = x∈IR : x<2A = x∈IR : x<-2⇒x∈(-∞ , -2)A = (-∞, -2)B =…

Q: Find the complement of the set given that U = {0, 1, 2, 3, 4, 5, 6, 7, 8}. (Enter your answers as a…

A: First we write {x | x W and x < 4} in roster form. Note: W=whole number.

Q: Show that a set {V1, ..., Vp} in R" is affinely dependent when p > n + 2.

Q: Which of the sets that follow are spanning sets forR3? Justify your answers. {(2, 1,−2)T, (−2,−1,…

Q: Find the glb and hub of the following sets. Which of these belongs to the set. (a) A = (b) B=…

Q: 2. Given A, B, and C are non-collinear points, draw the following or explain why it is impossible…

A: We have given three points A,B,C which are non colinear that is these three points does not lie…

Q: Determine whether the set S = {1, x², 6 + x²} spans P2. S spans P2. O s does not span P2.

A: P2 is the vector set of all polynomials with real coefficients of degree 2 or less. So 1+x is an…

Q: Find the Cartesian Product of the given sets: With A = {c, d, f} and B = { w, x}, find B x A.

A: A = {c, d, f} and B = {w, x}, B x A = { (w,c), (w,d), (w,f), (x,c), (x,d), (x,f) }

Q: Let U = {x | x is a letter in the word %3D GUADALARAJA}, where this is the universe set. Also, let M…

Q: Pick a set of five vertices of J and draw the subgraph induced by that set of vertices d J:

Q: Show every possible 1-1 correspondence between the following sets. {A,B} and {a,b}

A: The solution are next step is

Q: (10) Show that the set A = {a € Q : a² < 2 or a < 0} is a %3D cut.

Q: Find the union of the sets. {e, m, p, t, y}∪∅

A: we have to find the union of the sets. e,m,p,t,y∪∅

Q: Use only the definition of affine dependence to show that an indexed set {v1, v} in R" is affinely…

Q: 2. Show that the set 3 S = 3 2 2 2 2 spans all of R³ or find an element of R' not belonging to…

Q: Does the set S = {(1,2, 3), (0, 1, 2), (-2,0, 1)}span R³? %3D O Yes O No

Q: If X = {a,b, c}, let T1 = {0, X, {a}, {a,b}} and T2 = {0, X, {a}, {b, c}} . Find the smallest…

Q: Find the complement of the set given that U = {x | x I and −3 ≤ x ≤ 7}. (Enter your answers as a…

Q: In R with the cofinite topology, every preopen set is open

A: As we know that , In ℝ with discrete topology of every semi open set is open.

Q: Which of the sets that follow are spanning sets forR3? Justify your answers. {(1, 0, 0)T , (0, 1,…

Q: A set of ordered pairs in which each member of the set of first components corresponds to exactly…

Q: Suppose A={-1, 0, 4}.Find a set B such that A is equivalent to B.

A: Two sets A and B are said to be equivalent to each other if both the sets A and B have same number…

Q: The set {(a,b) : a EA and b EB} denoted by ...............

Q: A set L cR is convex if:

A: In this question, we have to find the correct option for the convex set L⊂Rn here we use the direct…

Q: Which of the sets that follow are spanning sets forR3? Justify your answers. {(2, 1,−2)T , (3,…

Q: Draw a Venn diagram for the symmetric difference of the sets A and B.

Q: Let 4, B, and C be sets. Show that а) (А — В) — С сA-C. b) (А — С) n (С- В) 3D0.

Q: Let X be a nonempty set with subsets, A, B, and C. Prove that A ∩ (B \ C) = (A ∩ B) \ (A ∩ B).

Q: For any metric space (X, d) and x EX, the singleton set (x) is closed. Select one: OTrue O False

Q: Consider the set Z in which the relation R is defined by aRb if and only if a + 3b is divisible by…

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

Q: Let (Z,t) be a cofinite topological space. The set {.-74,-72,-70,70,72,74,...} is

A: Given Z,τ be a co-finite topological space. Where, Z is the set of integers that is…

Q: Determine if the set S is span set of %3D R2x2. Solution:

Q: Determine whether or not the given set is (a) open,(b) connected , and (c) simply-connected. {(x,y)…

A: Determine whether or not the given set is (a) open,(b) connected , and (c) simply-connected. {(x,y)…

Q: Determine whether the set S = {−2x + x2, 8 + x3, −x2 + x3, −4 + x2} spans P3.

A: Given a set, S=-2x+x2,8+x3,-x2+x3,-4+x2 We need to determine whether S spans P3.

Q: If K is a compact subset of RP and z is a point of RP, then the set K, = {r+y :y € K} is also…

A: Given that K is a compact subset of ℝp and x is a point of ℝp. The objective is to show that…

Question

Suppose {p, p,, P3} is an affinely independent set in Rn and q is an arbitrary point in Rn. Show that the translated
set {Pi + q, P2 + q, P3 + q} is also affinely independent.

Expert Solution

Step 1

Here, {p₁,p₂,p₃} is an affinely independent set.

So, {p₁,p₂,p₃} are linearly independent.

Step 2

Consider the set { p₁+q, p₂+q,p₃+q}

Determine the difference of the elements of set.

(p₂+q)-(p₁+q)= p₂-p₁

(p₃+q)-(p₂+q)= p₃-p₂

For the elements of the set { p₁+q, p₂+q,p₃+q} to be linearly dependent, the differences,

p₂-p₁ and p₃-p₂ must be multiple of each other.

Step by step

Solved in 3 steps