3. Solve the system of congruences Show the steps used. 3x = 2 7x 3 8x7 mod 7 mod 11 mod 19.

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A: Given that  be two bases for the vector space  . and  .Now Hence Next given that  and a linear map

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Q: S₁ = 3 S₁ = 5 and and Sn+1 = √√10S₁-17 for n≥1. n Sn+l = S₁ + 2 7 for n ≥ 1.

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Q: 6. Let f: Q R be defined by f(x) Show that f is continuous. 0, :{ 1, = if x € (-∞, √2) nQ if x €…

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Q: 5. Consider X with the discrete metric. (a) Show that every subset of X is open and closed. (b) Show…

A: Consider X with the discrete metric. (a) Show that every subset of X is open and closed. (b) Show…

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A: Two straight lines rotate about two fixed points (-a, 0) and (a, 0) in anticlockwise sense. If they…

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Q: 1. Find all solutions of the congruence 5x+3x²+x+3 = 0 mod 30. You should do this by factoring the…

A: The congruence .To Find:Solution of the above congruence.

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Q: Let R be a ring and M a module over R. Let S be a non- empty set and let {x; : i E S} be a basis of…

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Q: (b) Let a.. and m be positive integers. Prove that if (a,m) = (b, m) = 1, then (ab, m) = 1.

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Q: Find Q for the QR factorization of A Q = Ex: 1.23 V1 = J]-[ 1 0 -3 0 2 -30 0 -10 3 -30, V3 = -2]…

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Q: 2. Verify that n Re(Στ;) = ΣRe z; j=1 n Im)zj) =) Imzj. j=1 j=1

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Q: Let f(x) := x² for x∊R, and let E := {x∊R : -1≤x≤0} and F := {x∊R : 0≤x≤1}. Show that E∩F = {0} and…

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