11. Find a basis of the following subspace of R4. W = all vectors of the form (a, b, c, d) where a + b – c + d = 0. (а) {(1,0, 0, —1), (0, 1,0, — 1), (0, 0, 1, 1)} (b) {(1,0,0, –1), (0, 1, 0, –1)} (c) {(1,0,0, –1), (0, 1,0, –1), (0,0, 1, –1), (0, 1, – 1,0)} (d) {(1,0,0, –1), (0, 1,0, –1), (0, 1, –1,0)} (е) {(1,0, —1,0), (0, 1,0, — 1), (0, 0, 1, —1)} 6. 6. 6.

Q: 2. How many vectors does any basis of of Max(a+2)(R) contain, if a = max1<i<10 a;?

A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

Q: Find a basis B for the span of the given vectors. B = [01-41] [51-10] [4191] 11

A: Basis for the span of the set of vectors: To find a basis for the span of a set of vectors, write…

Q: B = (1, x+1, x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of the…

A: The coordinate vector of v with respect to  is given by such that .(a) Given .Comparing the…

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

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Q: 7. v₁ = (0, 0, 1), V2 (0, 0, 1), V₂ = (7, 4, 11), V3 = (5, 3, 13) 8. V₁ = V1 (2, 0, 0, 0), v₂ = (0,…

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Q: 14. Let P₂ be the vector space of polynomials of degree ≤ 2. Let D = {1 + t, 1 − 5t, 2 + t²}. Check…

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Q: 3. Prove that the vectors u = (1, 1, 1), u = (1, 2, 1), and (1,3,-1) form a basis in R³. Find the…

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Q: 13. Let A = {a1,a2, a3} be an ordered basis for the real vector space V. (a) Find the coordinate…

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Q: 5.- Demonstrate whether the vectors of the following vector space are linearly dependent or linearly…

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Q: Express the vector (4, 7, -2) as a combination of the standard basis vectors i = (1, 0, 0), 3 = (0,…

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Q: The set B = {1+t², t + t², 1 + 2t + t²} is a basis for P₂. Find the coordinate vector of p(t) = 1 +…

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Q: 1a. Given vectors v₁ = (1, 0, 0) and v₂ : (1, 0, 0) and v₂ = (0, 1, 0) in R³, find a vector V3 such…

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Q: 1. Find the coordinates of vector w (1,2, 3) in the basis A which consists of T1 = (1, 1, 0), 72 =…

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Q: 4). Find all values of a for which the given vectors form basis for R' -(:) --() ---() a? u = and w…

A: A set B is said to be basis of any vector space if (1) it is linearly independent set. (2)B spans…

Q: Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 16.- Obtain a…

A: Given vectors are a=(1,3,-1), b=(-2,1,3), c=(3,2,1), and d=(1,-1,2).

Q: 3. Find a basis for the set of vectors in R³ in the plane x + 2y + z = 0.

A: Given equation of plane is: x+2y+z=0 To find: A basis for the set of vectors in ℝ3 in the given…

Q: 1. Show that the vectors (1, 1,0), (1, 1, 1) and (1,0, 0) are a basis of R3. Find the coefficients…

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Q: 3. Do the vectors (1, 1,0, 0), (1, -1,0,0), (0, 0, -1, 1) and (0, 0, -1, –1) form an orthogonal…

A: The solution is given as

Q: 3 2. (а) Do the vectors vị = -1 -1 form a basis for R³? , V3 = 1 > V2 = -I--- (b) Do the vectors vị…

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Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1,0,0)T., (2,0, 1,0), and (0, 0, 0, 1) form a…

A: The given set is .Now

Q: (a) Given S={(1,-5,4), (11,6,-1), (2,3,5)} the set of vectors in R³. Determine whether (i) S spans…

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Q: c) Consider the vector X₁. -3 = [³3] i. Express x₁ as a linear combination of the standard basis…

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Q: - Let B = {v1, V2, V3} be the ordered basis of R3 consisting of V1 = 1 V2 = - V3 = 1 Find the…

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Q: 5. Determine whether vectors u =(2,-6,-5), v = (3,8, 18) and w = (8,-6,7) will form a basis for R³.…

A: Basis is very important in linear algebra. A basis set always contains linearly independent vectors…

Q: Determine whether the following vectors in R' are linearly independent lineariy dependent: (i)…

A: As per our guidelines I am supposed to solve only one question. So kindly upload the other questions…

Q: 5. Let V = {(a, b, c, d): a + 3b-2c=0}. Show that (-3, 1, 0, 0), (2,0, 1, 0), and (0, 0, 0, 1) form…

A: 5) Given  that  Let, So we have  .Hence Noted that .Because  Hence basis for subspace V of  is

Q: Given the vectors V1 = (x, 1,1), V2 = (1, x, 1) and V3 = (1,1, x). S = { V1, V2, V3} of the set Find…

A: 3 vectors form a basis of R3, if they are linearly Independent. Vectors are linearly Independent if…

Q: 5. Consider V=R². Find the coordinates of = (10, 20) with respect to the ordered basis ß= [(1, 1),…

A: we will find the coordinate vector with respect to the given basis.

Q: 3. Let W = ((1,2,3,6), (4,–1,3,6), (5, 1, 6, 12)) %3D W2 = ((1,-1,1,1), (2,-1,4, 5)) %3D be…

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Q: Determine whether or not the set of vectors S-(. l where -(1,1.1), - (1,2.3).-(2,-1,1) form a basis…

A: The subset S is basis of vector space Rn over field R if  S spans Rn and  S is linearly independent…

Q: 1. (a) Determine whether the following three vectors v, = (0, 3, 1,-1), v2 = (6, 0, 5, 1) and vz =…

A: Solution Given v1=(0,3,1,-1) v2=(6,0,5,1) v3=(4,-7,1,3) in R4 We need to find the linearly dependent…

Q: If B = {(1,1,0), (0,1,1), (-1,0,2)} is a basis of R³, then the coordinate vector of v = (2,0,1) in…

A: Solve the following

Q: Q.2) For VR2 and B = {(1,2), (3, 4)"}, C = {(7,3), (4,2)"}; consider one vector v = = (1,0) ¹. •…

A:

Q: 12. Find a basis for the orthogonal complement of the row space of A: [1 0 2] A = 1 1 4 Split x =…

A: Orthogonal complement: Let W be a subspace of Rn. Its orthogonal complement is the subspace…

Q: 2. Consider the following sets of vectors. Show that each set (i) contains the zero vector, (ii) is…

A: The given sets are (a) W is the set of vectors of the form 3s, -2s, s. We have to show that  i Each…