Question

Find the length of the vector. $$\mathbf{v}=(2,0,-5,5)$$

   Find the length of the vector.
$$\mathbf{v}=(2,0,-5,5)$$

Elementary Linear Algebra

Elementary Linear Algebra

Ron Larson 8th Edition

Chapter 5, Problem 4

Instant Answer

Solved by Expert Varsha Aggarwal

02/18/2022

Step 1

So, for the vector $\mathbf{v}=(2,0,-5,5)$, we can write the length as $\sqrt{2^2 + 0^2 + (-5)^2 + 5^2}$. Show more…

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Find the length of the vector. $$\mathbf{v}=(2,0,-5,5)$$

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Key Concepts

Vector

A vector is an ordered collection of numbers that represents a point or a directed segment in a multidimensional space. Vectors are fundamental objects in linear algebra and are used to describe quantities that have both magnitude and direction.

Euclidean Norm

The Euclidean norm, also known as the length or magnitude of a vector, is calculated by taking the square root of the sum of the squares of the vector's components. It provides a measure of the distance from the origin to the point represented by the vector in Euclidean space.

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