O Find Hhe mahix A for T relative to the basis 8, where B' is made up of the baris vertors fand in pant (b).

Q: Let B = {v1,..., Vn} be an orthonormal basis for R". (a) Prove Parseval's Identity, that is, for any…

A: According to the given information,

Q: 4. Apply the principal axis transformation to the curve of second order -x2 + 6xy – y? – 22.x+ 18y –…

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Q: What is [v]B, the coordinates of v = with respect to the standard basis B : of R?? Ex: 5 : [v]B =

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Q: Consider P2 (R) together with inner product: Find an orthogonal basis for P2 (R). (p(z),9(2) = Г'р…

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Q: Find a basis for R^4 that includes these two vectors.

A: Solution: Given vectors are: v0=0342,  v1=1121 We know that the standard basis of ℝ4 is e1,e2,e3,e4…

Q: Explain why S i not a basis for P2. S = {1, 4x, -5 + x?, 3x} O sis linearly dependent. O s does not…

A: We have to find out

Q: Find the coordinate vector of p relative to the basis S = {p1, P2, P3 } for P2. p = 2 – 3x + 2x² ;…

A: Question from linear algebra.

Q: Let (vi..... vn) be an orthogonal basis of R". For any vectors x, y in R" show that (x- vi) (y vi)…

A: Given v1,v2,…,vn be an orthogonal basis of ℝn. Let x,y∈ℝn. Since v1,v2,…,vn is basis, therefore:…

Q: Let QE M,(R) be given such that the columns of Q form an orthonormal basis for R". Prove that Q'Q =…

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Q: Let S = {v1, v2} be a basis of IR? where vi = and What element of R? is determined by the linear V2…

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Q: Find out Vector S= { V, V2, V3} is the Basis por R. if VI : ( 3,1,-4), Vz C2,s,6), V3 - C1,4,8) %3D…

A: Here we have to find whether v1 , v2 , v3 are basis of R3 or  not.

Q: ,T If {v1, ..., Vn} is an orthonormal basis for R", then vịv¡ + · · ·+ vn Vn = I. True False

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Q: (и, из) for Find the coordinate vector of w relative to the basis S R². Let ui (5, –4), u2 = (3, 7),…

A: Solvig by au+bv=w

Q: Let T : R? → R? be defined by T x2 xi - x2 Let u = and C = V2 = Find T(u), the image of u under T.…

A: Given dataT: R2→R2 defined byTx1x2=x1x1-x2

Q: Given the bas is x, cwhere X= X,J for R3 2. 3. use the Gram - Schmidt process to transform the basie…

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Q: Given the following three vectors: Show that v1, v2, iz form a basis of R by proving that they are…

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Q: find the matna X for T elative to the basis B: T:R'R*, TG j) = (x-J,y-ta), 8'-{(1, -), CO 3)} I D

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Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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Q: Given the following vectors, let W Span{v, v2, vs}. v3 (a) ( . Is z in W? Why or why not? (b) ( Find…

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Q: (a) Find the coordinate vector of æ with respect to the ordered basis E = -2 of R3:

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Q: Find x in R2 whose coordinate vector relative to the basis B is [x]B =

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Q: Q. If B = {e, = the usual basis R2. Determine its dual basis. ?? ده رده را( = (D, 1)} is

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Q: Let TilP > Pz, the basis of NIT) T (ax²+bx+c) = 2Qx+ b. Then %3D is

A: Applying nullity definition we have

Q: 3) li) Find the dual basis {l, l} of the standard basis of IR". (i) Fiod th

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

Q: What is [A]B, the coordinates of A = | 3 with respect to the standard 8 1 0 0 1 basis B of R2x2? 0 0…

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Q: b: Construct the orthogonal basis of set T= {v1,v2, V3} for R3 Where v = 19 v2 = 7 V3 = |1 Express…

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Q: Show that the following set of vectors is a basis for M22: 5. 3 12 - 4 Let V be the space spanned by…

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am…

Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: Let TiPe s Pe, T(ax?+ bx+c) = 2Qx+ b. Then the basis of NIT)

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Q: Let TilPe ~> Pe, Tlax?+bx+c) = 2QX+ b %3D the basis of NIT) is True False

A: Applying nullity we have

Q: ow that B = {5+i, 2+i} is a basis for Q(i) whose elements are algebraic tegers. Why is ß not an…

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Q: Show that the vector space P, has the basis S = {1, x, x², x³}. %D

A: We have to solve given problem:

Q: Find the coordinate vector of a -2 with respect to the basis B %3D for R.

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Q: Find the coordinate vector of Prelative to the basis S = {P,P2P3} P1 = 1+ x + x, P2 = x + x²,P3 =…

A: Vector

Q: 10. Consider the plane 2x - 3y+4z 0. Find a basis B of this plane such that (B = for ū =

A: Solution:-

Q: Find

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Q: What is [p]B, the coordinates of p = 4+ 7x with respect to the standard basis B = {1, x} of P1? Ex:…

A:

Q: Let {v1, ... , vn} be an orthogonal basis for Rn and let W = span(v1, ... , vk)· Is it necessarily…

A:

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x², -1 – 6x + 7x2} || O sis linearly dependent.…

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Q: If {v1,..., Vn} is an orthonormal basis for R", then vịvi + · · ·+ vnvn = I. O True O False

A: Given, v1, v2, ..., vn is an orthogonal basis for Rn. then v1v1T+...+vnvnT=I It is True or False. To…

Q: Let B'- {1+2x, 3-x} And B = {1,x} be Basis for Pi a) s Find the Transilion matrır Pine from B' toB…

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Q: Q: Find a representation of Jp(t)> at a time t +0 using the ordered basis {|e1>, ]e2>, ]e3> }.

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Q: Let V = span {V1, V2}, where V1 and V2 = 1 2 Find a basis S for R3 that includes vi and v2.

A: Let V  = span { v1 , v2}  where   v1= 102 and v2 = 111 Find a basis S for R3 that includes v1 and…

Q: Let B={ }].OH} be basis for IR %3D Find [v]o where 6- 563

A: Given β=3-30,22-1,114 be basis for ℝ3 v=15-93 To find vβ

Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x2, -1 – 7x + 8x²} O sis linearly dependent. O…

A:

Q: Let TilPe > Pz , T (ax?+bx+c) = 2Qx+ b. Then the basis of NIT) is

A: Just use a definition of Nullity of transformation.

Q: Let B= { }],19} be basis for IR. %3D Find [v]g where V= 15

A: Given :                          Basis  B = 3-30, 22-1, 114 and V = 15-93…

Q: 10)Define TE L(R²) by T(x, y) = (41x + 7y,-20x + 74y). Verify that the basis of T %3D with respect…

A: Question 10. The detailed solution is as follows below:

Q: thogonal basis for W:

A: Orthogonal decomposition of vector

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.