Consider the subspace S of the Euclidean inner product space R* spanned by the vectors v₁=(1,1,1,1), v₂=(1,1,2,4), v₂=(1,2,-4,− 3) . Find an orthonormal basis of S. O A. None in the given list ³. {(², ₁-3,1), (1,2,-4,-3). (4,2,1,1)} OC {(1,1,1,1),(-1,-1,0.2), (1.3.-6.2)} OD. {(1,1,1,1),(1,1,2,4),(1,2,-4,-3)} OE OB ((1.1.2.4).(-1.-1.0.2).(-1)}

Q: The set B = {1-1², 2t-12², 1-1-1²) is a basis for P2. Find the coordinate vector of p(t) = 3 +…

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Q: 11. Find a basis of the following subspace of R4. all vectors of the form (a, b, c, d) where a + b –…

A: The solution is given as

Q: The set F = {1+t,t +t, 1+2t+t2} is a basis for P₂. Find the coordinate vector of p(t)= 3 +t-4t²…

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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: Extend the vectors [1 3 -1 -1]' and [0 -1 1 1]' to a basis for the following vector space. V = 6- 2a…

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Q: 1. Assume that (u₁, U2, U3, U4) is an orthogonal basis for for R¹, where = (1, 2, 1, 1), u₂ = (-2,…

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Q: Suppose we have a set of vectors S = {V1, V2, V3} CR4. Which one of the following is a true…

A: Solution :- According to this given question

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Q: Let W be the subspace of RS spanned by the vectors = (1,2,3,-1,2) and v= (2,4,7,2,-1). A basis of…

A: We have to solve given problem:

Q: Consider the vector space generated by [0, 1, –1, –1], [1,0, 2, 4], [1, 2, –4, 0]. Find an…

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Q: Is the following set of vectors S = {v,, V2. V3} basis for R³ space? Where, a. v = (3,1,–4), v2 =…

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Q: Let ----0-- -2 = Show that {V₁, V2, V3} forms an orthogonal basis in R³. Express W= as a linear…

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Q: be the bases in  R³ T={,,},     S={,,} determine the matrix of transicion of T to S

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Q: 2. Let ū = (-1, 2, 1), ở = (1, – 1,–1) and w = (2, 3, 0). Find the coordinates of (2,4,4) with…

A: Using gauss Jordan elimination method to find the value.

Q: The set B = {1+t², -t+t², 1+2t+t²} is a basis for P₂. Find the coordinate vector of p(t) = 5-6t+13t²…

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Q: Find a basis for the space S of vectors ( a, b, c, d) with a+ c + d = 0 and also for the space T…

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Q: Consider the subspace S of the space Euclidean inner product (1.1.1.1), ₂(1.1.2.4). v,= (1.2,-4,-3).…

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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: Show that {u₁, u2} is an orthogonal basis for R². Then express x as a linear combination of the u's.…

A: Given:u1​=[2−6​],u2​=[124​],x=[2−2​]  Step 1: Check OrthogonalityTwo vectors u1​ and u2​ are…

Q: In the Euclidean inner product space R4 with an orthonormal basis B={-(1,1,1,1), ½-(1,1, − 1,− 1), —…

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Q: Let P2 be the vector space of polynomials of degree 2 or less. Consider the following two ordered…

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Q: Mark the following statements true or false. If false, give an explanation of why it is false. (a)…

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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: Show that B = {v1, v2, v3} is an orthogonal basis for R3: v1 = (3,−3,0), v2 = (2,2,−1), v3 =…

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Q: Determine whether S is a basis for the indicated vector space. S = {(0, 0, 0), (5, 2, 3), (3, 6, 5)}…

A: Given set is S = { (0, 0, 0), (5, 2, 3), (3, 6, 5) }

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…