Let R have the Euclidean inner product. Express the vector w = (0, 0, -2, -1) in the form w=w + w, where w; lies in the space W spanned by the vectors u (0, 1. 2, -2) and uz = (2, 0, 0, -1), and w; is orthogonal to W. Round your answers to 2 decimal places. Edit Edit

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A: Distance = 4.41

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Q: -2 Show whether or not the vector bs is a linear combination of the vectors a, = az = and az = that…

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Q: 3. Determine if the vectors work. -2 are linearly independent. Show all 0 1

A: Step 1:The given vectors are: ⎣⎢⎡​1−23​⎦⎥⎤​,⎣⎢⎡​111​⎦⎥⎤​ and ⎣⎢⎡​0−11​⎦⎥⎤​ To determine whether the…

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Q: 5. v₁ = (1, 0, 0), V₂ = (0, -2, 0), V3 = (0, 0, 3)

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A: To find the given questions related to span of a set :-

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.