Y1 Y2 ER3 [Y3. (x, y) 2x1y1 + X2Y2+5x3Y3, for x = |X3 (a) Find a basis for the orthogonal complement of 5 with respect to the function (·, ·).

Q: Please show me the steps to solve this question. It is a part of vector calculus.

A: Value of the integral is 9/16Explanation:

Q: 2. Let v, = (1,2,1), v2 = (2,9,0), v3 = (3,3,4). Show first that S = {v1, V2, V3} %3D is a basis for…

A: 1. A finite set of vectors v1,v2,...,vn of a vector space V over a field F is said to be linearly…

Q: (5) Let V=R2. For (1, 1), (2, 32) EV and c ER, define addition and scalar multiplication operations…

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Q: Let V=R². For (₁, ₂), (V₁, V₂) € V and a ER define vector addition by (41, 14₂) H (V₁, V₂) := (U₁ +…

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Q: Let 6 2 A =| 9 5 11 8 L = 3 1 and 1 4 U = | 0 2 -1 Find scalars r, s, t, and p so that LU = A.

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Q: 5. Let ū = (0,2, 1), ở = (-1,0, 2) and w = (2,3,0). Find the coordinates of (2,2,2) with respect to…

A: This question is related to vector space. Solve in 2nd step .

Q: Consider the data: (zo, f(xo)), (₁, f(x1)), (2, f(x₂)), (#3, f(#3))).\\ The Lagrange basis…

A: Lix=x-x0x-x1·..x-xi-1x-xi+1·...x-xnxi-x0xi-x1·..xi-xi-1xi-xi+1·...xi-xn∴Lixj=0     for i≠j1     for…

Q: et B = · 9, (x − 1)², 3x³) be an ordered basis for P3. Find the coordinate vector of (x) = 3x³ + 2x²…

A: Coordinate vector

Q: Assume that in a chart (U, r) of a surface E, the shape operator is represented by the matrix for…

A: Given: θ=011b from some b belongs to R with respect to the basis (ru,rv)

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: Find an orthonormal basis of the plane z1 + 7z2 - 13 = 0. {

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Q: Let V be the vector space of functions spanned by B = {bị = 6 sin æ + 4 cos a, b2 = 2 sin æ + 7 cos…

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Q: Give the coordinates of the harmonic conjugate of (–1, –1, 0) with respect to (1, 1, 1) and (3, 3,…

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Q: Let c1 (t) = ei + 7 sin(t)j + t*k and c2 (t) = e-Sti + 5 cos(t)j – 7t*k. (Enter your solution as a…

A: Given: Let c1(t)=e5ti+7sintj+t4k and c2(t)=e-5ti+5cos(t)j-7t4k. To Find:      ddt[c1(t)+c2(t)]

Q: 3. Let T : R² → R² be defined by T = X Y -x+y x-y

A: 3. Given that  be defined by:

Q: V is the linear span of the polynomials a =x' + 2x – 2x + 1, ß=x' + 3x² - x+4, y = 2x +x - 7x – 7…

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Q: Consider the ordered basis B = {(1,-1,0), (1, 1, 1), (0, 1, 1)} of R³. the coordinate vector v =…

A: Consider the ordered basis B=1,-1,0, 1,1,1, 0,1,1 of ℝ3.   To Give: The coordinate vector v=-2,-1,0…

Q: 7. Let S = Show that span S = R' and find a basis for R' consisting of vectors from S.

A: Span of vector : Let us consider a vector space V then the set S is aid to be the span of V if the…

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: Find the dimension and a basis of U = r2s+t 0 -3r s-t r, s, tER

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Q: Let ū = -4î + 4ĵ – 3k and i = î – 25 + 2k. (a) Let w = proj, ū. Compute w. (b) Compute u-w and show…

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Q: 3) Let T d b }]= la + 1b + 1c + 5d + 2e +2f la + 2b + 0c + 5d + 3e + 1f 3a + 4b +3c + 17d+ 8e +6f…

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Q: Expand x = (a, b, c, d) with respect to the orthogonal basis of: 2 -1 1 Vị = V2 -2 3 Express your…

A: Note: Observe that the given orthogonal basis spans only two dimension subspace of ℝ4, therefore the…

Q: 1 Defined in P,(R), p(x)=1,q(x)=x- and h(x) =x² -: -x+- 6. Investigate whether the vectors are…

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Q: Let P2(R) be the vector space of polynomials over R up to degree 2. Consider {1+x – 2x?, –1 +x+x², 1…

A: Consider the provided question, Given that,  B=1+x-2x2, -1+x+x2, 1-x+x2B'=1-3x+x2, 1-3x-2x2,…

Q: The vector x = H vector [2]8 = [2] A 1 B2 C3 in R² relative to the orthogonal basis B = What is the…

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Q: Draw the projection of b onto a and also compute it from p = îa: -=[] a = (a) b = cose 3] sin and…

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Q: 2. Let B₁ be the basis r²e, ze, e of V = span(r²e², xe, x), and B₂ be the basis is H.6 of w that the…

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Q: = Consider the basis B₁ = {(1, 0, 0), (1, 1, 0), (1, 1, 1)} of R³ and the basis B₂: – 2), (3, -1)}…

A: