The set B=(v= (1,1,1),u=(0,0, - 3),w=(2,2,0)) IS: OA Linearly independent in R3. OBa subspaces of R. OC Linearly dependent in R3. ODa basis of R.

Q: (2) Find a basis for the subspace W = {(a +c, 2a – b, 3a – 26 – c,b+ 2c) | a, b, c € R} of R.

A: We need to find the basis for the given subspace:

Q: Let V = U® W and let {u̟,u2, ... , uk } be a basis for the subspace U and {W1,W2, ..., Wk } be a…

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Q: (2) Find a basis for the subspace W = {(a+c,2a – 6, 3a – 26 – c, b + 2c) | a, b, c E R} of R4

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Q: Prove that E = {(x, y, z) E R°, x + y+ z = 0} is a subspace of R3 and find a basis of E. Deduce…

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Q: The set W of all 2x3 matrices of the form a I where c = a + b, is a la 0 subspace of M23. a. Find a…

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Q: Find an orthogonal basis of the subspace of spanned by the vectors 目目 。啡3, 。翻 3 -9 (а) (b) (c) -2…

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Q: In the vector space P, of polynomials of degree at most two, 2' transition of the matrix from the…

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Q: Find the orthogonal decomposition of v with respect to the subspace W. (That is, write v as w + u…

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Q: Let W be the subspace of R$ spanned by the vectors w,=(2, 2, -1, 0, 1), w2=(-1, -1, 2, -3, 1),…

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Q: Find a basis for the subspace of P2 spanned by the given vectors.  1 + x, x2, -2 + 2x2, -3x

A: Basis are (1, 1,0), (0, 0,1), (-2, 0,2), (0, -3, 0)

Q: The vector x is in a subspace H with a basis B = {b, ,b2}. Find the B-coordinate vector of x. 1 -3…

A: According to the given information, X is a vector in a subspace H with basis B. it is required to…

Q: Let W {(a,b, c, d)| 5a - c = 0 } be a subspace of R*. Then a basis for W is

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Q: Let W be the subspace of R^3 spanned by the given vectors v1 = (1,1,1), v2 = (1,2,-3), and v3 =…

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Q: The vector x is in a subspace H with a basis B= {b, ,b,}. Find the B-coordinate vector of x. 1 -3 -…

A: We will solve a system not equations to find the B-coordinate vector. The detailed solution is as…

Q: Prove that the set of vectors of the form (a, b, c) where b = a +c is a subspace of R³.

A: According to the given information, it is required to prove that:

Q: and let W the subspace of R" spanned by i and v. Find a basis of W-, the orthogonal complement of W…

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Q: If W is a subspace of R" of dimension k with a basis {v1,e,2,..., v%} then W Range(|v1 v2 vn)). ...…

A: Given: Let W be a subspace of Rn and dimk=k Let B be a basis of k then B=k Also B is a linearly…

Q: Find an orthogonal basis for the subspace {(x, y, z) E R³ | x + 4y – 2z = 0} -

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Q: Find an orthogonal basis of the subspace of spanned by the vectors (a) (b) -2 (c) (d) 234

A: To find the orthogonal basis of the subspace of spanned by the vectors 234 and 123 Consider that the…

Q: Let W be the subspace spanned by the given vectors. Find a basis for W-. 1 -1 1 W1 W2 -5 -2 1

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Q: Find an orthogonal basis for the subspace H of IR that is spanned by the vectors 1 1 1 -2 1 V1 = V2…

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Q: Let W {(a, b, c, d)| a – 5 b = 0 } be a subspace of R*. Then a basis for W is

A: The given subspace of R4 is W={ ( a , b  ,c , d ) | a - 5 b = 0 } Let x=( a, b , c , d ) be in W…

Q: 3.8 Using the Gram-Schmidt method, turn the basis B = (b1, b2) of a two- dimensional subspace U C R…

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Q: Let 1 -3 and let W the subspace of R' spanned by u and v. Find a basis of W-, the orthogonal…

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Q: Show that the set T= {(a, b, c, d): 2a-3b+Sc-d=0} is a subspace of R'.

A: Given T=abcd∈ℝ4:2a-3b+5c-d=0 Let A be a 1×4 matrix defined by: A=2-35-1 Then the equation…

Q: In the vector space P of polynomials of degree at most two, the second column of the matrix of…

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Q: 2. Consider the set of matrices W : b : а,b€ R a (a) Show that W is a subspace of M22. (b) Find a…

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Q: Let H span {(-11,0, –5), (–3,0, –1), (–2,0, –1)}. A basis for the subspace H C R³ is { vector

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Q: Let W be the subspace spanned by the given vectors. Find a basis for W⊥

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Q: The vector x is in a subspace H with a basis B= {b,,b,}. Find the B-coordinate vector of x. 1 - 4 -…

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Q: Consider the vectors v1, v2, ..., Um in R". Is span (01,..., īm) necessarily a subspace of R" ?…

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Q: Let W be the subspace of R spanned by the vectors -2 and Find the matrix A of the orthogonal…

A: Given that  W be the subspace of ℝ2 spanned by the vectors                           1-21  and…

Q: Let W = {(x,y, z): x – 6y + 8z = 0 } be a subspace of R³, Then a basis for W is: O (2,1,0),(-8,0,1)…

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Q: Find a basis for the subspace of R* consisting of all vectors of the form (a, b, c, d) where c = a +…

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Q: If W is a subspace of ℝ4 whose dimension is 2 then is any set of 2 vector is a basis for W

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Q: Let W be a subspace of R". A set of vectors {v1, ..., Úp} in W is defined to be a basis of W if {v1,…

A: Let ℝn be a vector space. Let W be a subspace of ℝn. Then,  is W={v1→,......,vp→}a basis. Definition…

Q: Let 5 Find a basis of the subspace of R4 consisting of all vectors perpendicular to v.

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Q: Let W be the subspace of R having basis {(0, –1, 3), (1, 1, 2)}. Determine the projections of the…

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Q: Let v, = (43 2 1), v2 = (-2 0 -1 0), V3 = (0 3 0 1) a) Find the subspace of R" spanned by these…

A: The given vectors are: v1=4, 3, 2, 1, v2=-2, 0, -1, 0 and v3=0, 3, 0, 1 The subspace W spanned by…

Q: The vector x is in a subspace H with a basis B = {b, ,b,}. Find the B-coordinate vector of x. 1 - 2…

A: Given that, b1=14-2; b2=-2-73; x=15-3 Since B = b1, b2 is the basis, xB is the linear combination of…

Q: Let H be the set of all vectors of the form (a – 3b, b – a, a, b) where a and b are arbitrary…

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Q: (2) Find a basis for the subspace W%3D { (а+c, 2a — b, За — 2b — с, b + 2с) | а, b, с € R} of R4.

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Q: The subspace W={( 0 -b ); a, b E R} has the basis set : —а а Select one: 0 0 a. S={(,), 1 0 0 0 0 O…

A: For a set to be a basis of a subspace. i) it must be independent. ii) it should generate the…

Q: In the vector space P, of polynomials of degree at most two, the third column of the matrix of…

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Q: In each part, find a basis for the given subspace of R, and state its dimension. a) All vectors of…

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Q: The vector x is in a subspace H with a basis B = {b, ,b,}. Find the B-coordinate vector of x. 2 b1…

A: We have given the basis   B=b1,b2where b1=21 , b2=-13   and we have a vector x = 49in a subspace H…

Q: Investigate the dimension of the following subspace of R*. All vectors of the form (a,b,c,d), where…

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Q: Find a basis and the dimension of the subspace W = {(a+1)x+(2-b)x²; a,b e R} of P,.

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Q: . Let W be the subspace of R' generated by the vectors (1, –2, 5, –3), (2, 3, 1, –4) an (3, 8, –3,…

A: Consider the metrix A with given three vector as row…

Q: Find a basis of the subspace of R“ that consists of all vectors perpendicular to both 目-日 and

A: Given that, This can be written as,