3- Suppose u, v EV and||u|| = ||v|| = 1 and = 1. Prove that u = v

Q: Let B = {b₁,b2} and = {C₁, C₂}. Find [v] and [v]. B 10 -9 [v] Ⓡ [v] 8 -7 -6 -5 -4 -3 -2 -1 6- 5 4 3…

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Q: Given the N-length sequence x[n]: 10 8 7 6 5 3 2 G find the following values of x[n]: a. [8] =…

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Q: Find the change of basis matrix [B]&• 2 B = { []}]} <= { [4] []} C 7 8 23 10 71 40 4 10 8 40

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Q: c) d² y dt² +2 dy dt + y = 4t, y(0) = 0, y'(0)=5

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Q: bits are needed.

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Q: 1. Solve the initial value problem on the real line Utt - Uzz = sin x U(x,0) = 0 Ut(x,0): = sin x

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Q: Find the vector determined by 18 || = B = {[.]. 9 6 12 3 9 2 -8 " where B = 3 [-]

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions ×₁…

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Q: 5 Estimate the area between the function h(x) = + 5 and the x-axis on the interval [3, 7] using 4…

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A: Use iteration to guess an explicit formula for the sequence.

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Q: 2. Solve Utt- c²UTT for x = [0, π] with the boundary conditions and the initial conditions = 0 U₂…

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Q: Let a : V → W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2,…

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Q: r₁= [3 -1 0], (a) (₁, ₂) (b) (r1,73) (c) (r2, r3) r₂ = [-2 0 1], T3 = [1 -2 4].

A: (a)   &lt; r1 , r2 &gt; =  [ -3  1  0 ] . [ -2  0  1 ]                        = 6 + 0 + 0…

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Q: Let f,g: RR be differentiable everywhere. Assume that g is one-to-one function. Show that f(g(x…

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Q: (a) (₁, ₂) (b) (r1,73) (c) (r2,73) r₁= [3 -1 0], (d) r1 xr2 (e) ri Xr3 (f) r₂ × 3 r₂ = [-2 0 1], T3…

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Q: . Let f:R" →R be a differentiable convex function. Consider the following problem: (P) min f(x) s.t.…

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Q: Prove by induction that Vn N 72 n(n+1)(2n - 2) Σ(i²-i) = 6 i=1

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Q: Let f(x) be a bounded, non-negative differentiable function on [0, ∞). Prove that the length of f(x)…

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