31. Let R* have the Euclidean inner product. Use the Gram- Schmidt process to transform the basis {u,, u2, u3, u4} into an orthonormal basis. u, = (0, 2, 1,0), u; = (1, 2,0, –1), u, = (1,0,0, 1) u, = (1, – 1,0, 0),

Q: Let V = .e R such that a + b =0 and W = R such that e= d. Find basis for V nw. Select one: O a.…

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Q: Find a basis for the plane 4 + 3y + 5z = 0 in R. %3D

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Q: Use the Gram-Schmidt process to transform the basis ü, = (1,0,0),ü, = (3,7,-2),ū; = (0,4,1) into…

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Q: Let V= Ips Let B= Ź(1?,3)(0,2),(-2,0,D}be a basis for V. Find the courdinate vector Of the rector X…

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Q: Let R⁴ have a product in Euclidean. Use the Gram Schmidt process to convert the basis (u1, u2, u3,…

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Q: Show that {u,, u2, uz) is an orthogonal basis for R. Then express x as a linear combination of the…

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Q: (- _-----«s) If {ƒ1, ..., fn} is an orthogonal basis of R¹ and U = span{f₁,..., fm}, show that U =…

A: We will be proving the statement using basic definitions of Orthogonal Basis of Rn .

Q: Let W= span{(1,2,-1,0),(2,2,0,1),(1,1,-1,0)}. Use Gram Schmidt to find an orthogonal basis for W.

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Q: b) Using the basis S in (a), find [T)s if ū = (2, i, 2 – i).

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Q: 2. Prove that the following vectors |v1) = (1, 1, 0) |v2) = (1, 2, 0) |v3) = (0, 1, 2) span C3. Are…

A: Given that,                    |v1> = 1 , 1 , 0                    |v2> = 1 , 2 , 0…

Q: 1. Vector i = (1,-1,2) (in standard basis) 2. The linear transform (in standard basis) T: R’-→R'…

A: Given: x¯=1,-1,2 The linear transformation T:ℝ3→ℝ3 defined by…

Q: 4. (a) Let L be the line in R' spanned by the vector (1,1, 1, 1). Find a basis for the orthogonal…

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Q: 1. Consider R³ with the dot product. Use the Gram-Schmidt process to transform the basis {(1,-1,-1),…

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Q: Use the Gram-Schmidt process to convert ((0, 1, 1, 0)", (1, 1, 1, 0)", (0, 1, 1, 1)'] to an…

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Q: Apply the Gram-Schmidt process to transform the basis vectors V1= (1,1,1), V2 = (0,1,1), V3 =…

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Q: 4. Let R³ be equipped with the dot product and let B = {(1, 1, 1), (0,2,0), (2, 0, 1)}. B is a basis…

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Q: 2. Apply the Gramm-Schmidt orthogonalization process to the vectors [1, 3, 2] and [1, 0, 1] in order…

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Q: Find the coordinates of (2, 3, 4, – 1) with respect to the basis B = {(1, 1, 1, 2), (1, –1, 0, 0),…

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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: 5. Use the Gram-Schmidt process to transform the basis B = {(1, −1, 1), (1, 0, 1), (1, 1, 2)} for…

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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: 15. Assume that the vector space R³ has the Euclidean inner product. Apply the Gram-Schmidt process…

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Q: let R3 have the Euclidean inner product and use the Gram-Schmidt process to transform the 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: Use the Gram-Schmidt process to find an orthonormal basis for Span ([2, 1, 2, 4], [0,-1, -2,01¹).

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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: 8. Let W = Span{v1, v2}. Find an orthonormal basis for W. Vị = -2 , V1 = 4 2

A: An orthonormal basis for an inner product space V with finite dimension is a basis for V whose…

Q: The following vectors form a basis for R. Use these vectors in the Gram-Schmidt process to construct…

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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: 9. Consider the orthonormal basis S for R³ S = (v₁,v₂,v,} where v₁ = (0,1,0) and v₁ = Let u = V₂ = =…

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Q: 2. Let the inner product on vector space V be (u,v)= uvdz. Use the Gram- Schmidt process to…

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Q: Use the Gram-Schmidt process to transform the given basis {w1, W2, W3} into an orthogonal basis…

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