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: 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: . 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: 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

A: Given that

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

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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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