In Exercises 7-10, show that {u₁, u₂} or {u₁, U2, U3} is an orthogonal basis for R² or R³, respectively. Then express x as a linear combination of the u's. 7. 6 --G--0-×-Q = and and x = 4 = 2 -3 9

Q: [4] Find the coordinate vector [x] of the vector x = 5 (4-2) the basis = The coordinate vector [x] =…

A: Please refer to the solution in next step.

Q: Show that {₁, ₂} or {₁, ₂, 3) is an orthogonal basis for R² or R³. Find the coordinate of with…

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Q: Determine whether (v₁, v2, v3) is a basis for ³. 1 0, V3 = -4 22 7) v₁ = -2 4, V2 = -8

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Q: 2.) Determine whether S = {G.1).(1.0).(2,12,6)} is a basis for R. If it is write u = (6,3,6) as a…

A: Determine whether S=23, 52, 1, 1, 32, 0, 2, 12, 6 is a basis for ℝ3. A set of linearly independent…

Q: Let B = {A1, A2, A3, A4} and B2 = {C1, C2. Cs, C4} when : %3D %3D A3 A4 = 0 0 C; - (; }).c- (? :).c-…

A: By Bartleby policy I supposed to solve first 3 subparts.But I am solving all subparts.

Q: If {a, x} is a basis of solutions of x?y" + axy' + by = 0, then a = (А) —2 (В) 2 (C) -3 (D) 3 (E)…

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Q: 21 4. Determine if the vectors 2 5 1 -3. 6. LO. constitutes a basis for R^3.

A: Concept to be used:In the space R3, any set of three linearly independent vectors forms a basis of…

Q: {B].[B]} Vector w expressed in ß is w = Vector v expressed in basis a = = {[]·[3]} Answer: 133 Wa is…

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Q: . Determine if the vectors (3,2,0) , (-3,0,1) , and (1,1,–9) span all of R’ . Do these vectors form…

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Q: Show that the vectors a, (1, 0, 0), a2 = (1, 1,0), a, = (1, 1, 1) form a basis of C'(C).

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Q: 5. Given the bases B and C, and the given vector in one the bases, find the coordinate vector in the…

A: Please see the below pictures for detailed solution.

Q: 5. The conjugate of 2√7-√√3 is: a) √3-2√7 b)-2√7 + √3 d) 2√7 + √3 c) √7 + √3 6. In R³, the standard…

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Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

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Q: 127 (68) -100 -4 23 B = v= 27 is an orthogonal basis of R³. Find [v]⁄·

A: (.) Given orthogonal basis is,           and  vector (.) Orthogonal basis: A basis  is called an…

Q: 3) Let C be a basis that contains vectors (1 + (-1) x + 1x² + 1x³), (1 + 2x + 2x² + (−1) x³), (1 +…

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Q: –10 S = l2] ] 13 2. 2.

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Q: За + 6b — с ба — 26 — 2с - Find a basis for H = : а, b, с €R -9a + 56 + 3c | -3a + b+ c

A: Given H=3a+6b−c6a−2b−2c−9a+5b+3c−3a+b+c:a,b,c∈R We have to find the basis for H. First write the…

Q: 4. In R² a) Draw the grid corresponding to the basis 3 = 3.72] b) A certain vector v in R² has…

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Q: Suppose {u, } form an orthogonal basis in R2 and y = 2ū - 7 where u = (8) 6 If W = Span{}, what is…

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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: Describe all solutions of Ax 0 in parametric vector form, where A is row equivalent to the given…

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Q: 10 - Which set is an orthogonal basis containing å = (3,4) ? { (3,4),(-3,4)} mo { (3,4),(-4,3) } {…

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Q: In Exercises 1-4, find the vector x determined by the given coordinate vector [x] and the given…

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Q: Suppose that a₁,a2,..., a, form a basis of R" and y = ₁²₁ +2₂₂ + ... + n Anan with 2; = 0. Prove…

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Q: Explain why S is not a basis for M2,2- $-{::::)) OS is linearly dependent. S does not span M2,2- OS…

A: Given: S=0110, 1001 and M2,2. We have to explain why S is not a basis of M2,2.

Q: 6. -4 Új = -5 U2 = 3 form a basis for R’ if and only if k #

A: Three vectors form the basis of ℝ3 if and only if the determinant of the matrix formed by the…

Q: Given the ordered basis B=A₁ -1 0 -[5], 42 - [8 A₂ -2 6 (4]} 8 16 -33 -1 3 [¹].4 A4 0 -9 A3 - find…

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Q: 22. Find a basis for R4 that contains the vectors (3, 2, 3, 3) and (5, 4, 5, 5)

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Q: 2.) Determine whether S = is a basis for R³. If it is write u = (6,3,6) as a linear combination of…

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Q: ,B = the standard basis, C - {[; -}-[; :)-8)-[: 9]} in 22 (a) Find the coordinate vectors [A] and…

A: The standard basis B for M22 is {e1,e2,e3,e4}.

Q: If B= {(1,1,0), (0,1,1), (−1,0,2)} is a basis of R³, then the coordinate vector of v= (8, -5, 3) in…

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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: Find all possible real numbers a, b, c, d E R such that form a basis B= (v.w) for R² that satisfies…

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Q: In Exercises 25-28, u and v are binary vectors. Find u + v in each case. 25. u= 26. u= 0--0 10

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