Exercise 5.12. Let L be an ideal in C[x₁,...,xn], and be a monomial order. Let G = {9₁,..., 9p} be a Gröbner basis of L. Prove that if f € L then there exists a g; so that in_(f) is divisible by in_(9₁).

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Q: Find the degree and a basis of the extension field Q(v3, v7) Q(V3 + v7). over

A: This question is from field theory's topic extension of field. Solution is given below.

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Q: 1. We let P(R) denote the set of all polynomials of degree at most n with real coefficients. Let T =…

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Q: Let V1 = [0, 0, 5, 0], V, = [3, 4, 0, 0] and V3 = [4, 0, – 2, – 4] Use the Gram-Schmidt procedure to…

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