(b) Note that for a E R, v(a) E N. Show that R is an Euclidean domain with respect to the norm v. (c) Show that a is a unit in R if and only if v(a) = 1.

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A: If x is a unit vector then:

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Q: 5. Find a vector æ € R³ such that ||Ax – || is minimal, where [1 1 -2] 1 and b:= 2 1 1

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Q: (b) Is (R2,d) a metric space, where d((x.y1).(x2.y2)) 1x1-x2l; for all (x, , y1 ), (x2 2) E R2 ?…

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Q: [:] [] Find c so that the vectors and are parallel.

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Q: LG, CF, and AU are concurrent.

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Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: Let X be vector space of all ordered pairs. Show that ||x || = |x1| + |x2] defined norm on X %3D

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Q: Let U = span(1, 1, 0), (1, 1, 1)). Find a vector u E U such that Ilu – (1, 0, 0)|| is as small as…

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Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

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A: Topic:- addition of vector

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Q: Find the Euclidean norm of the given vector. Hint: 7 = 49, 24? = 576 V = 24 ||v|| = Ex: 1

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