Consider P2 (R) together with inner product: Find an orthogonal basis for P2 (R). (p(z),9(2) = Г'р [*p(z)q(z) dz.

Q: If {e, xe", e2 is a basis of solutions of y" + ay" + by + cy = 0, %3D then a =

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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: 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: Find the matrix A' for T relative to the basis B'. A' = T: R² → R², T(x, y) = (x − y, y - 2x), B' =…

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Q: 6. Let p(t) = ² + 1 and g(t) = t - 4 be vectors in P2 with inner product (f(t), g(t)) = f(t)g(t) dt.…

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Q: Set V = {(x, y) | x ER, YER}. Define addition of vectors by the rule (x, y) + (x, y) = (y + y',x+x')…

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Q: Find the matrix A' for T relative to the basis B'. Tea T: R² → R², T(x, y) = (x − y, y − 3x), B' =…

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Q: Let B = {(1, 1), (2, 3)} and B′ = {(5, 2), (1, 3)} be two bases for R2. [T]B= 2 3 4 7 (a) Find (T…

A: please see the next step for solution

Q: Q2) (a) Use the definition = ]f(t)g(t)dt in T0,1] to find the components of f(t)=2+t in the…

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Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: Find a basis for null(T), where T : R^3 → R^2 is defined by T (x, y, z) = (−7x + 2y − 5z, 4x + 9y +…

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Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: 3. (а) Consider the vectors ū = i – 6j + 4k, ở = 2i – 5j – 3k and w = 6i – 2j + 3k Show that ū x (T…

A: Use the formula for determining the cross product of two vectors  Substitute the values given and…

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: 4. Given two bases (b) = transformation y : R² → R² with respect to the basis (f) and let X, be a…

A: Given two bases b=b1,b2 and f=f1,f2 of ℝ2  where  b1=12, b2=34, f1=11, f2=23 Let Af be a matrix of a…

Q: . Show that (x, y) = 4x1y1 – 7x2y2 for vectors x = (x1, x2) and y = (y1 y2) in R2 defines an inner…

A: Given two vectors x and y in R2. We need to show that the given function in x and y defines an inner…

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: 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: Given the operator S on the vector space R₁ [x] given by S (a+bx) = -a+b+ (at 2b) x A) What is SC1)…

A: We know that Pn is the vector space of all the polynomials of degree n+1 and the basis for this…

Q: 3) Let S contain vectors of the form f(x) = a + bx + cx² + dx³ : f(-2) = 0 and f'(-4)= 0: Then a…

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Q: Consider the inner product on R2 defined by ((x, x2), (y, y2)) = x11 + 4x2y2. Which of the following…

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Q: Find the domain of the vector functions, r(t), listed below. You may use "-INF" for -∞o and use…

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Let T: R² R² be defined by T Let u = T(u): ¹([^])=[^²=²] = X2 H | amnet C = { v₁ = [!] > v₂ = [2]}…

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Q: : R^3-->R^3,T(x, y, z) = ( x + y, y + z, x - z)  (a)the basis of  the range(T) (b)determine if T…

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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: Dim (3) Ex. consider T: IR ³ -> R² T( 9₁, 92, ₁₁, 95) = (artastas, 92-94)}. T NCT) = ((a., 92, 93,…

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Q: (3) Let L be the line y 2r in the plane. Find a matrix C such hat for every vector H plane, the…

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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: The Hermite polynomials form an orthogonal (not orthonormal) basis with this inner product: (Hm[Hn)…

A: Given:                                   fx=x3…

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: 6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z,…

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Q: If {e", xe", e2a is a basis of solutions of y" + ay" + by' + cy = 0, then a = (A) -2 (В) 2 (С) —4.…

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Q: (a) Find the best approximation to ✅ by a vector of W. (b) Write as the sum of a vector in W and a…

A: note : Since you have posted question with multiple sub parts, we will provide the solution only to…

Q: (ii) Let W = span{ } v = and The orthogonal projection of v onto W is projw(v) = and the component…

A: Given : v=-43-7    and W=span{ -2-32 , -3-1-2 } Aim: to find (a) projw(v)      ,and   (b) perpw(v)

Q: 6. Project the vector b = (1, 4, 2) onto the plane S that contains the vectors a₁ = (1, 2, 1) and a2…

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Q: Find the matrix A' for T relative to the basis B'. A' = T: R² → R², T(x, y) = (x - y, y - 2x), B' =…

A: “Since you have asked multiple questions, we will solve the first question for you.If you want any…