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.

Q: 12] and a3 = -20 4 -------- Let a₁ = h 5 2 The set {a1, a2, a3} will span R³ unless h = 0

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Q: Let P1, P2, P3, .. , P78 be some coplanar points with k lines on the same plane. If exactly two line…

A: Given,  P1, P2,P3,...,P78 be some coplanar points with k lines on the same plane. If exactly…

Q: Question 3  Show that if A and B are sets with A ⊆ B, then A ∩ B = B.  Full explain this question…

A: Show that if A and B are sets with A ⊆ B, then A ∩ B = A.

Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u -(2/3)v - (1/6)w = (0, 0, 0), can…

A: A set of vectors u1, u2, ……, un is said to be linearly independent if c1u1+c2u2+……+cnun=0 implies…

Q: Determine the dimension of the span of each set. 6 3 12 - A = span ({0}) 2 - -1 4 20 10 40 dim (A) =…

A: Here sets A,B and C are given. We find dim(A),dim(B) and dim(C).

Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

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Q: a) Show that the set S = {(1, 2, 3), (0, 1, 2), (– 2, 0, 1)} spans R³. b) Determine whether the set…

A: See the attachment.

Q: Prove that B = (0,1) is NOT a compact set.

A: To prove that (0,1) is not a compact set.

Q: d) Suppose X = {1,2, 3} and Y = {5,6}. The number of elements of the set P(X× Y) =

A: Elements in X = 3. Elements in Y = 2 Elements in X × Y = 3 × 2 = 6

Q: Suppose that A and B are subsets of S. Express symmetric difference of A and B (AtriangleB) in terms…

A: It is given that A and B are subsets of S. The symmetric difference A and B is defined as the set of…

Q: {₁,...,} is linearly independent if and only if {₁,...,} is an orthogonal set. True False

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Q: Determine whether the given set is linearly independent.

A: We will check that given set is linearly independent or not using definition of linear independency.…

Q: Show that for any arrow, you can pick an axis such that the projection of the arrow on that axis…

A: The statement is true, and to see why, let's consider an arbitrary arrow in three-dimensional space.…

Q: Let U = {1,5,7,8, 10, 12, 14, 17, 18}. Deter mine the comple ment of the set (7,10, 17). The…

A: Given the set  U = { 1, 5, 7, 8, 10, 12, 14, 17, 18} And a subset A = {7, 10, 17}  We need to…

Q: Find a topology in which the point x = 5 is an open set.

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Q: Consider the following set of ordered pairs of the elements of a set A = {0, 1, 2, 3, 4} of numbers…

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

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Q: Consider the subsets [0, 1] and [3, 4] of R, the set of all real numbers with the euclidean…

A: Consider the subsets [0, 1] and [3, 4] of R, the set of all real numbers with theeuclidean topology.…

Q: Let A, B, C be subsets of X. show that Av (Bnc) - (AUB)n (AUC) AnCBUC) = (ANB)~ (ANC)

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Q: Why is the set {91 +124t² - 61t³, 66 − 58t +93t², 22 + 248t — 87t² } not a basis for P3(R)? Select…

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Q: (FNB) UC'

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Q: Consider the following set of ordered pairs of the elements of a set A = {1,2, 3, 4} of numbers and…

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Q: Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly…

A: We have to check whether given set of vectors linearly independent or linearly dependent by known…