EXERCISE 7.4 For 1 and 2, determine the dimension of the indicated subspace of R4 1.) The set of all vectors of the form (ab.c.o) 2.) The set of all vectors of the form (aaaa)

Q: Find a basis for the subspace S of R4 consisting of all vectors of the form (a + b, a − b + 2c, b,…

A: We have to find the basis for the subspace S. We have to find the dimension of S.

Q: Suppose that U and V are both subspaces of R . Prove that their intersection U ∩ V = {v : v ∈ U…

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Q: find a basis for the given subspace of R3, and state its dimension. All vectors of the form (a, b,…

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

A: Let V be a vector space. H is said to be a subspace of V. If  H is a subset of V. H is closed with…

Q: Use Theorem 5.2.1 to determine which of the following are subspaces of R3. (a) all vectors of the…

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Q: Is the set of all vectors of the formb, where a, b, and c are any real numbers with a +b+c > 0, a…

A: A subset W of Rn is a subspace of Rn if it satisfies Non-emptiness:  The zero vector is in W.…

Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: a a subspace of R³? Show your proof. La+2b] the set of vectors of the form

A: Given the set of vectors of the form aba+2b , which can also be expressed as:             W =…

Q: a. . Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

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Q: Use Theorem 5.2.1 to determine which of the following are subspaces of p3. (a) all vectors of the…

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Q: Is the set of vectors of the form [a,b,a+2b] a subspace of R^3

A: If W is a non empty subset of the vector V, then W is a subspace of V if and only if the following…

Q: . Is the set of all vectors of the form b where a, b, and c are any real numbers with a +b+c> 0, a…

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Q: Find the dimension of the subspace U={[a+c, b+c, a+2c+b] | a, b, c in R} Select one: a. 2 b. 4 c. 1…

A: We have given a subspace ,  U = a + c , b + c , a + 2c + b / a , b , c ∈ ℝ We need to find dimension…

Q: Consider the sets of vectors of the following form. Prove that they are subspaces of R3. 1.  (a,…

A: Solve the following

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: 4. Use the definition of a subspace to prove that the set V:= :, y, z E R, y+ : 0 is a subspace of…

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Q: {{},} Let W be the subspace of R3 spanned by write j = |3 3 as the sum of a vector in W and a vector…

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Q: a Is the set of all vectors of the formb. where a, b, and c are any real numbers with a +b+c>0, a…

A: In this question, the given set W is defined as W=abc ∈R3 s.t. a+b+c>0, for all a,b, c in R}  To…

Q: a Is the set of vectors of the form a subspace of R³? Show your proof. La+2b

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Q: Find the orthogonal projection of V = nto the subspace W of R* spanned by Uj = U2 = Uz = -6/4 -6/4 w…

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Q: 2. Determine if the set S consisting of vectors of the form b where abc = 0 is a subspace of R³.…

A: No, S is not  a subsapce of ℝ3. Explanation: Here,  s1=110 and s2=001 belong to set S. Then,…

Q: show what W = {(a,0,b)| a,b E R)  is a subspace of R^3

A: Given : W={(a,0,b)|a,b∈R}   To Show : W is subspace of R3

Q: Find a basis for the subspace of R" spanned by the vectors 1 1 .2. -3. .6.

A: Use the given vectors.

Q: Use Theorem 4.2.1 to determine whether the set of all vectors of the form (0,0,m) form a subspace of…

A: Option first is correct

Q: Consider the three vectors V1 = (1,0,0, –1), v2 = (0, 1, 1, 0), V3 = (1, 1, 1, 1). Let W be the…

A: Given that W be a subspace of R4 spanned by the vectors. v1=(1,0,0,-1), v2=(0,1,1,0), v3=(1,1,1,1)…

Q: Show that W = {(a, 0, b)la, b = R} is a subspace of R³.

A: As per guidelines we are supposed to solve the maximum first questions only .kindly post another…

Q: {] Find a basis for the subspace U = | a, b, c € R } of R³. Please justify your answer. -6

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Q: Consider the subspace W = {(a, b, c) E R³ : a – 26 – 3c = 0} of R³. (b) Is {(5, 1, 1)} a basis for…

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Q: (a) Determine whether the set of all vectors of the form (a,b,c), where b= a+c, is a subspace of R³.…

A: Consider the subset S of ℝ3 defined as, S=(a,b,c)∈ℝ3 | b=a+c Take  a1,a2,a3,b1,b2,b3…

Q: a Is the set of vectors of the form La+2b] subspace of R3? Show your proof. a

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Q: . Let W be the subspace of R3 spanned by the vectors vj=(1,0,7), v2=(6,1,7), and V3=(14,-1,13). Find…

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Q: 9

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Q: Use Theorem 4.2.1 to determine whether the set of all vectors of the form (m,n,1) form a subspace e…

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Q: () (:) 1 (2) Let u = Describe the set H of the vectors that are orthogonal to u. Is H a subspace?…

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Q: Consider the vectors: V1 = (2,0,0,-2), |V2 = (–14 –7,–12,54). V3 = (0,1 1|-6) V4 =…

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Q: Find the distance from the point x = (1, 5, –4) of R³ to the subspace W consisting of all vectors of…

A: First we will find out the orthogonal basis for the subspace W. Then we calculate the orthogonal…

Q: a . Is the set of all vectors of the form b, where a and b are any real numbers, a subspace W of R?…

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Q: {{} } 5. Let W be the subspace of R³ spanned by write j= |3 as the sum of a vector in W and a vector…

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Q: In Exercise , find the orthogonal projection of v onto the subspace W spanned by the vectors u?.…

A: v=123 , u1=2-21 and u2=-114

Q: 6. (a) Find a basis for the subspace of R' spanned by 1 4 7 -5 7 4 w = 4 -5 (b) Using part (a),…

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Q: Use Theorem 4.2.1 to determine whether the set of all vectors of the form (a,0,0) form a subspace of…

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Q: In Exercise , find the orthogonal projection of v onto the subspace W spanned by the vectors u?.…

A: Given :           v = 31-2 ; u1 = 111 ; u2 = 1-10   To find an orthogonal projection of v onto the…

Q: Determine: if W = the set of all vectors in R^2 whose second component is the square of the first.…

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Q: 2. Find the dimension of the subspace of R³ spanned by the following set of vectors. {(1,5, 6),…

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Q: 6. (a) Determine whether the set of all vectors of the form (a,b,c), where b = a+c, is a subspace of…

A: To show the subset W is a subspace , we need to show that (a) 0∈W (b) For every w1 , w2∈W , we have…

Q: Q2. Check if the following points lies on the subspace U spanned by the vectors = [2 -1 2]', x2 = [0…

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Q: Find a basis for the subspace of R spanned by the following vectors. 7 4 2 2 18 -3 6 6 18 18 12 14…

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Q: Find an orthogonal basis of the subspace of spanned by the vectors 目 目 [2] (a) (b) 3 (c) (d) 12 2 3…

A: We have to find an orthogonal basis of the subspace.