Find the power set of: a) {w, {x}, {y, z}} b) {1,2,7} с) (3,(1,4)}

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A: We have to prove that the number of elements in any SList of depth p is . Notice that the…

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A: Is AB is congruent AD what theorem is used to prove this?

Q: Prove that the four points P(2, ;1, 1), Q(1, 3, ; 2), R((2, 1, ; 3) and S(3, 2, 0) are coplanar

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Q: 4. Prove that triangle ABC with A(3, 6), B(4, -1), C(-2, 1) shown below is isosceles.

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Q: The projection of u onto v is given by projvu = ________.

A: The projection of u onto v is given by projvu = compvu.

Q: 3. Prove that sinOtcos=1.

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Q: 4 Q: Is A- (: ) dingonalizable ? %3D

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Q: Show that M=abcd ab,cdeR is the set 1) all ) X) matrics.shou that it is under adlition and scaler…

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Q: Prove by mathematical induction: X n (U-, Y) = U=1(X nY), for V n E Z* – {1} and sets X,Y,,Y2,. Yp-…

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Q: (a) Find the length of the projection of w onto v given that w = (4,7) and v = (1,1).

A: Given: w=4i+7j, v=i+j we know that projectionp→ of w onto v is given by p→=w.→v→v→2v→

Q: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

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Q: A, is skew-symmetric, then prove that (B B + B, B') An = . Ajk = 0. %3D

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Q: Let T cofinite topology on R and Y={5,6,7} find Ty?

A: We have to construct subspace topology with respect to the cofinite topology

Q: Be M, N subsets of space W. Then span (MUN) = span (M) +span (N)- %3D

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Q: prove that for any arrangement of 31 figures on a chessboard, there are 3 places on which there are…

A: As there are 64 places on a chessboard, after filling 31 figures, there will be 33 vacant places.…

Q: Show that w is in span(B).

A: Given that: B=120,120, w=1188 To show that w is in span(B).

Q: What is the dimension of P,?

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Q: Create the matrir U from U by scaling each column of U so that it has norm 1. Show that the matrir U…

A: We need to scale the columns of U so that the norm of the new matrix is equal to 1. Consider U=xy…

Q: Is S = {a + b√(2) : a, b ∈ ℤ} dense in ℝ?

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Q: 4. Let A Sketch the collection of points Ar for i in the unit square.

A: Let A=1101. Sketch collection of points Ax¯ for x¯ in the unit square. Matrices maps a polygon to a…

Q: a subipace of Masa And, the set s-{(:),(;:), () #) w {():x, YaR} i) W = {Ğ ): x, Question 3 -{:9),(?…

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Q: Let W = Lin and U= Lin 2 (a) Show that R' = W U. Explain.

A: Note:- As per our guidelines, we can answer the first part of this problem as all the parts are…

Q: LBe M, N subsets of space W. Then span (MUN) = span (M) + span (N)“ %3D

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Q: IFA and B have 6 and 9 elements each, what is the minimum number of elements Aunion B?*

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Q: Suppose X has n elements and Y has m elements. How many bijections X → Y are there?

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A: The number of shape are given above in the question.

Q: 1. Decide if the following statement is True or False: %3D Let A1, A2, ..., Ak E Mnxn(R) be such…

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Q: . Six equal rods AB, BC, CD, DE, FE and FA are each of weight W and are freely jointed at there…

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Q: Prove that if A is skew-symmetric matrir, Q = et is orthogonal.

A: c) To prove:- If A is skew-symmetric matrix , Q=eAt is orthogonal. Proof:- Ais skew-symmetric matrix…

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Q: 6. Given plane M parallel to plane K. A and Care points in M, and B and D are points in K such that…

A: As per bartleby guidelines only 1 question is answered, please upload each question separately: It…

Q: Given the bases B = {u,u2} and B'= {u', u'2} for R?, where and u'= The transition mat rix Pg-g' from…

A: Linear transformation problem.....

Q: .Six equal rods AB, BC, CD, DE, FE and FA are each of weight W and are freely jointed at there…

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Q: In R4, let S = span{(1, 1, 1, 1)T ,(1, 2, 1, 3)T }. Find S⊥.

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Q: De = system consider the foll lution exists for = 2, µ ations exist for = 5, µ = on for 2 = 6, µ = 7

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Q: Find the intersection of the sets. {w, y, z}∩∅

A: Given, w,y,z∩∅we have to find intersection of the sets.

Q: 2. Let W = Span {u1, u2, uz3, U4, U5, U6}, where 4 1 , U5 = Uj = U2 = u3 = ,u4 = U6 = 2 2. 4 What is…

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Q: Prove that u, v, and w are all in span(u, u + v, u + v + w).

A: To Determine: prove that u ,v and w are all in span (u,u+v,u+v+w). Given:  we have(u,u+v,u+v+w)…

Q: 11. Square ABCD with verlices 4-1, 3), B(O, 6), q3, 5), and D(2, 2): yx A B. D:

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Q: Let S = {(1,1), (1, 2), (2, 1), (3, 2), (3,3)}. Consider the polytope conv(S). Write this set as {r…

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Q: (b) Using Venn Diagram to prove that (A U B)e = A° N B° ?

A: To prove the following using Venn diagram A∪Bc=Ac∩Bc First consider the left hand side  Set A

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Q: b) Give a partition which divides I = [1,2] into n equal parts. %3D

A: Consider the Interval  [1,2]

Q: Theorem. A rectangle R with side lengths 1 and x, where x is irra- tional, cannot be “tiled" by…

A: Without using the concept of linear algebra you can proof this. Let length of rectangle= 1 Unit…