Let u and v be two vectors in R°. Determine the most general condition under which {u, v, u × v} forms a basis for R³.

Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

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Q: Find the coordinate vector of p relative to {p,» P;» P3} for P,. the basis S =

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Q: Let x, y, and z be vectors in Cn and let a and B be complex scalars. Show that a ( z, x) +B ( z,y )…

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Q: For the vectors given below, show that U = {u1, U2, u3} is an orthogonal basis of R³ 3 2 Uj = |-3 U2…

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Q: Find the vector X (in standard coordinates) determined by the given coordinate vector xB and the…

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Q: 21. Find the coordinate vector of x = with respect to the basis B = {v1, V2, V3} where vi =|1 V2 =…

A: Write x in linear combination of v1 , v2 , v3

Q: { be a basis for R? . Find the vector æ if [æ]R =| 3 Let B 8 x = x = 6. x = x = H 00

A: Given that B=11,21 be the basis for R2. We have to find vector x if xB=23. Since, xB=23 Hence,…

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: Find the coordinate vector of P relative to the basis S = {p1.P2,P3} %3D P1 = 1 + x + x*, pP2 = x +…

A: First I have written a short note about coordinate vector of a vector relative to a basis and then…

Q: Let u and v be two orthogonal and unitary vectors. Prove that ||u – v|| = v2.

A: Given:   Let u→ is a unit vector means that u2=1         v→ is a unit vector means that v2=1   u→…

Q: Consider the basis D = {(1, 1, -1), (2, 1, 3), (-1, 2, 1)} of R3 and the vector v = (1, 1, 1) in R3.…

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Q: Compute  the  coordinate  vector  of  v with  respect  to  given ordered  basis  S  for  V . V is P1…

A: Given: v→=t+4 Ordered basis for v→ :  S = {t + 1, t − 2}

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: For each of the B bases below, represent the vectors in the coordinate system of the C basis. 3= а.

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Q: Find the coordinate vector of p relative to the basis S : {P1, P2, P3} for P2. p = 15 – 21x + 12x²;…

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Q: Consider the basis B of R consisting of vectors and Find x in R whose coordinate vector relative to…

A: Basis is defined as the linearly independent set that span a vector space V. Any vector of V can be…

Q: Find the coordinate vector [x]g of x relative to the given basis B= {b, , b2}. 3 2 b, ,b2 2 -7 - 5

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Q: Consider vectors a = (2, -8), b = (-1, 4), andc = 0. Determine the non-zero scalars a and B such…

A: Consider vectors a=(2,-8) , b=(-1,4) and c=0. We have to determine the non-zero scalars alpha and…

Q: Suppose M is the set of all real column vectors in R whose components are equal, then the basis for…

A: Given that M is the set of all real column vectors in R4 whose components are equal. We need to find…

Q: Given the set of vectors determine whether the set of vectors is a basis for R

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Q: Find the vector projection of B= 61+ij+2k onto A=1-2j-2k and scalar component of B in the direction…

A: projba = a.ba2b now, <a> = 6i→ + 3j→ + 2k→ <b> = (i→ -2j→-2k→) so, a.b = (6i→+3j→+2k→).…

Q: Consider the basis B of R consisting of vectors and 3 Find a in R? whose coordinate vector relative…

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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: to = [0 3 4 2]" v = [1 1 2 1]"

A: Handwriting solution.  { v0, v1, e1, e4} forms a basis for R4.

Q: Find the coordinate vector of v = [2 -7 7] relative to the ordered basis B = ( [1 0 1], [0 1 1], [2…

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Q: Consider the basis B of R? consisting of vectors and Find i in R? whose coordinate vector relative…

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Q: Let vectors u, v, w be a basis in V . Show that u + v + w, v + w, w is also a basis in V .

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Q: Let W = {ax? + (b-a)x + (a+b)| a, b e R}. Find a basis for V and find the coordinate vector for v =…

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Q: Find the coordinate vector of = -1 with respect to the basis B = for IR3. 2 B

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Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

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

A: Vector

Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. -2 B = ,…

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Q: Find the coordinate vector of p(x) = 5 - 2x + 4x² with respect to the basis B = (1 + x, 1 – X, x?}…

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Q: |Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = (2,–4,5). %3D %3D a) Are the vectors linearly…

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Q: For any vectors U, V and scalars a, b, prove that (a) (b) (aU) × (bV) = ab(U × V) (aU) · (bV) = ab(U…

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Q: Find the vector x determined by the given coordinate vector [x]pand the given basis B. [x]g

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Q: Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = (2,–4,5). 7.. a) Are the vectors linearly…

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Q: Find a basis for the space spanned by the given vectors, vl.,., v5. [M]

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Q: Find the vector x determined by the given coordinate vector [x]gand the given basis B. B= , [x]g =

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Q: .Let W = {ax? + (b-a)x + (a+b)| a, be R}. Find a basis for V and find the coordinate vector for v =…

A: find basis of V then will find coordinate

Q: In P, consider the basis B- {6,6} where 1 %23 b2 I – 4 Task Find the coordinates of vector w = 2z +…

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Q: :Consider the basis B of IR? consisting of vectors and 3 Find i in R? whose coordinate vector…

A: The given basis B for ℝ2 is: B=-75, -12 Find x→ in ℝ2 whose relative to the basis B is: x→B=3-5 Let…

Q: Given an orthogonal basis B and a vector v, find the B-coordinate vector of v. V 8. b) B =

A: Let B=v1,v2,…,vn be a basis for a vector space V and v be any vector in V. The vector v can be…

Q: . Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x +2, 2x…

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Q: Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = a) Are the vectors linearly independent or…

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Q: Given vectors v1 = (3,0,0), v2 = (1,2,0), and v3 = (2,–4,5). %3D a) Are the vectors linearly…

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Q: Write x as the sum of two vectors, one in Span {u,,u,,u3) and one in Span (uA. Assume that (u,,.u}…

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Q: Find the coordinates of vector u=(4,5) with respect to linear basis ((2,1),(1,-1) ? a. 2 b. 3 • 2 O…

A: Here we use linear combination to solve this

Q: Show that the given vectors form an ortho­gonal basis for R2 or R3• Give the coordinate vector [w]of…

A: Orthogonal basis:        Let v1,v2,.....,vn be linearly independent vectors in Rn, if v1,v2,.....,vn…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.