If G C P(S) has the finite intersection property, then there is a filter F on S such that G C F.
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Q: answer is wrong
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- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).Consider the matched filter solution discussed in the book:H(f ) = α (V (f )∗e^−j2πf t0 / SX (f ))Suppose that there is some open set of frequencies A such that for all f ∈ A, SX (f ) = 0 butV (f ) ̸ = 0. In this case, the solution above is undefined. What should we do to design the filter?If f(t)=t2 and g(t)=t, then the Wronskian W(f,g)(t) is: (A)-t2 (B) t-t2 (C) t (D) t2
- The main point of this exercise is to use Green’s Theorem to deduce a specialcase of the change of variable formula. Let U, V ⊆ R2 be path connected open sets and letG : U → V be one-to-one and C2such that the derivate DG(u) is invertible for all u ∈ U.Let T ⊆ U be a regular region with piecewise smooth boundary, and let S = G(T). Solve A B CIf n<m then every linear map T: IRn -> IRm is one-to-one. Is this statement true or false?Let f(x, y, z) = x2y + y2z. Use the Chain Rule to calculate af /as and af /at (in terms of sand t), where x=s+1, y=st, z=2s-1
- Let T : V --> W be linear, b ϵ W, and K = {x ϵ V: T (x) = b} be nonempty. Prove that if s ϵ K, then K = { s} + N (T).Prove that the multiplication map · : ℤ/n × ℤ/n → ℤ/n given by [x] · [y] = [xy] is well-defined.Let Qc(x) = x2 + c. Prove that if c < 1/4, there is a unique µ > 1 suchthat Qc is topologically conjugate to Fµ(x) = µx(1 − x) via a map of theform h(x) = αx + β.
