Let 1 € R be an Euclidean domain with the strictly positive Euclidean norm p : R \ {0} → N. Assume that p is multiplicative, i.e. p(ab) = p(a)p(b). Show that if a € R is a unit, then ø(a) = 1. (Hint: first show that p(1) = 1)

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A: We will prove the given statement.

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A: Given:

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Q: In Question,determine whether the definition gives a norm.

A: p(x)=p(0)+p(1)-p(0) for p(x) in P1

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Q: Examples 1) X = R with the norm |x|| = |x| x ER is normed space %3D

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Q: See picture

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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A: Please check step 2 for the solution.

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Q: Then ||-|| is a norm on R.

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.