4. Prove that ū = (1,0, 1), ở = (2, 2, –1) and w = (-2,3,0) are a basis for R. Use these three vectors to construct an orthogonal basis for R³.

Q: 4. Let {V1,... , Vn} be an orthogonal basis of R". For any vectors x, y in R" show that (x · V;) (y…

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Q: 2, Xz} is a basis of V, (R). show that {, +X, X2 + X3, X3 +Xi} is also a basis of V, (R),

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Q: Show that ?? = {(1,2,3), (−1, −1,1), (5, −4,1)} is an orthogonal basis of ℝ3, and use the Fourier…

A: Definition: A subset of a vector space V is linearly independent, if  Theorem: If is a orthogonal…

Q: Write down a basis for the vector space L(R", R).

A: Given vector space is the finite dimensional vector space of dimension m.

Q: The Gram-Schmidt process transforms the basis u=(1, 2), U2 =(6, 2) of R into the orthogonal basis…

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Q: (i, 2, 3i), v = Co over C. Are these vectors linearly independent? Can they form a basis 5.…

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Q: Q2. Leb u, and v be two livearly ondependent vecetors in R? Do thiy necussavily form a basis of R?

A: We have to write about vector u and v

Q: Let B be the basis of R? consisting of the vectors 4 -2 and let C be the basis consisting of 3 2…

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Q: 1- The vectors x, = (2,1, –4), x2 = (-3,4,1) and x3 = (2, –1,3) %3D %3D in R3, are A: represent a…

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Q: The vectors u, v, w have the coordinates (-6, 2, 1), (2. -1,0) and (7. -2, -1) respectively relative…

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Q: Let S = {v1, v2} be a basis of IR? where vi = and What element of R? is determined by the linear V2…

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Q: Find a basis of R that contains the vectors X = (1,1,1,1) and Y = (1,1,0,1).

A: Given Vectors X =(1,1,1,1) and Y = (1,1,0,1) Now determine the orthogonal basis for R4

Q: Show that fu,, u,) is an orthogonal basis for R?. Then express x as a linear combination of the u's.…

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Q: 4. Present the standard basis vectors e, and ez in R? as linear combinations of (3, 1) and (1, 3).

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Q: 5/ Find the coordinates of x = with respect to the basis consisting of uj = (1, 3, 2), u2 = (2,…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the matrix for T relative to the basis B, and use Theorem 8.5.2 to compute the matrix for T…

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Q: Let S = {V1, V2} be a basis of R? where v1 and v2 = -3 What element of R? is determined by the…

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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: (a) Find the coordinate vector of æ with respect to the ordered basis E = -2 of R3:

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Q: Show that the vectors (1, 1, 2), (1,2,5), (5,3,4) of R'(R do not form a basis of R'(R).

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Q: Show that in an n-dimensional vector space X, the representation of any x as a linear combination of…

A: The given problem is related with linear algebra. We have to show that in an n-dimensional vector…

Q: Let e1, e2, e3, e4, ē5, e6} be the standard basis in R°. Find the length of the vector * = 471+…

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Q: 15. Use the Gram-Schmidt process to transform the basis {r1, x2, a3, T4} into an orthogonal basis…

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Q: 3 2 1 Let u [-]--[-]-[] -3 V 2 and w= 1 0 -1 4 (a) Show that B = {u, v, w} is an orthogonal basis.

A: The given vectors are:  u=3-30, v=22-1, w=114. (a) To show: {u,v,w} is an orthogonal basis. (b) To…

Q: Show that {u, U2}, {u1,u2, U3} is an orthogonal basis for R? or R°, respectively. Then express x as…

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Q: Show that S = {(i, 0, 0), (i, i, 0), (0,0, i)} is a basis for C

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Q: 5. Determine whether the following three vectors v, = (1, 2, 3, 4), = (0, 1, 0, -1) and v, = (1, 3,…

A: To determine the given vectors form of basis for or not.

Q: Consider an inner product on two P3 vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(1)g(1) + f(2)g(2):…

A: Since you have posted multiple subpart question, we will solve the first three sub parts for you. If…

Q: If {f1, . . . , fn} is an orthogonal basis of R^n and U = span{f1, . . . , fm}, show that U^⊥ =…

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

Q: Find an orthogonal basis for R3 that contains the vector

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Q: Prove that the vectors (1, 1, 0),(1, 2, 3) and (2, −1, 5) form a basis for R3

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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: The Gram-Schmidt process transformsthe basis u1=(-3,1), u2=(7, 1) of R´ into the orthogonal basis…

A: Orthogonal set problem....

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: 2. Find a basis for R that includes the vectors and 2

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Q: Let {v1, ... , vn} be an orthogonal basis for Rn and let W = span(v1, ... , vk)· Is it necessarily…

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Q: Find the matrix for T relative to the basis B, and use Theorem 8.5.2 to compute the matrix for T…

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Q: Show that B = {1,1 – x,2 – 4x + x²,6 – 18x + 9x² – x³} is a basis for P3(R). Hint: Recall that…

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Q: Which of the following is a basis for the vector space R3?

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Q: Let {f1, f2, f3} be the dual basis of {e1, €2, €3} for R³, where e₁ = (1, 1, 1), €₂=(1,1,−1), Find…

A: Given basis are e1,e2,e3 of R3 where e1=1,1,1e2=1,1,-1e3=1,-1,-1 Its dual basis are f1,f2,f3 We have…

Q: 2- Show whether the set of vectors S={ ,,} is a basis of R3 ?

A: Given the set of vectorsS={<3,2,2>,<−1,2,1>,<0,1,0>}

Q: Write x as the sum of two vectors, one in Span {u, ,u2.u3} and one in Span fu4}. Assume that {u,…

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Q: Show that the vectors (1, 1, 2), (1, 2, 5), (5, 3, 4) of R'(R) do not form a basis of R'(R).

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Q: 2. Construct a basis for T2,2(R²) and prove that it is a basis.

A: To find the basis of I2×2ℝ2. The set of all 2×2 matrices over ℝ. Let us claim that…

Q: suppose that x↓1,..,x↓(n-1) are linearly independent vectors in R^n and also x↓n is notin the span…

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Q: Explain why S is not a basis for P,. S = {1 – x, 1 – x2, -1 – 7x + 8x²} O sis linearly dependent. O…

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Q: 2) Suppose the vı, V2, V3, V4 is a basis for a vector space V. Prove that vị + v2, Vz + V3, V3 + V4,…

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Q: 1- The vectors x, = (2,1, -4), x2 = (-3,4,1) and x3 = (2, –1,3) in R3, are %3D A: represent a basis…

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Q: Show that (u₁. U₂. u) is an orthogonal basis for R³. Then express x as a linear combination of the…

A: Answer is in next step. please give a like !!