# Keyword Analysis & Research: what makes vectors linearly independent

## Keyword Research: People who searched what makes vectors linearly independent also searched

Are vectors linearly independent iff they form a basis?

The three vectors are not linearly independent. In general, n vectors in Rn form a basis if they are the column vectors of an invertible matrix. Basis for a subspace 1 2 The vectors 1 and 2 span a plane in R3 but they cannot form a basis 2 5 for R3. Given a space, every basis for that space has the same number of vec­

Are two vectors having equal magnitude?

Two vectors are equal if they have the same length (magnitude) and direction. Examples: 1. Let u be the vector represented by the directed line segment from R = (-4, 2) to S = (-1, 6) a) Find the magnitude of u. b) Find the component form of the vector.

Does linearly independent imply all elements are orthogonal?

linearly independent (Adjective) (Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero. Does linearly independent imply all elements are orthogonal? Vectors which are orthogonal to each other are linearly independent. But this does not imply that all linearly independent vectors are also orthogonal.

Is orthonormal set of vectors a linearly independent set?

every orthonormal set is linearly independent every orthonormal set is linearly independent Theorem: An orthonormal setof vectors in an inner product spaceis linearly independent. Proof. We denote by ⟨⋅,⋅⟩the inner productof L. Let Sbe an orthonormal set of vectors.