The word basis is singular. The plural is bases.
1,250
Scripture will often form the basis for the day.
EEx. 35 basis points would be .0035.
The plural form of basis is bases(prononounced bayseez).
The dimension of a space is defined as the number of vectors in its basis. Assuming your vectors are 1,2,1,0 0,1,-2,0 2,2,1,0 and 3,5,1,0 (extra zeros because you are in R4) then you must first check to see if they are linearly indepent. If all the vectors are linearly independent then the subspace defined by those vectors has a dimension 4, as there are 4 vectors in the basis.
Yes. This is the basis of cartesian vector notation. With cartesian coordinates, vectors in 2D are represented by two vectors, those in 3D are represented by three. Vectors are generally represented by three vectors, but even if the vector was not in an axial plane, it would be possible to represent the vector as the sum of two vectors at right angles to eachother.
It can be the basis of the trig functions because the hypotenuse, which is the radius, is 1. For related reasons, it can represent unit vectors in any direction.
No it is not. It's possible to have to have a set of vectors that are linearly dependent but still Span R^3. Same holds true for reverse. Linear Independence does not guarantee Span R^3. IF both conditions are met then that set of vectors is called the Basis for R^3. So, for a set of vectors, S, to be a Basis it must be:(1) Linearly Independent(2) Span S = R^3.This means that both conditions are independent.
A plane has no vertices, so you can't. Pick one or three spicks (points) in the plane, usually at the basis vectors, for its label.
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
Vectors of the arthropod.
there are two types of vectors cloning vector and expression vectors.
Two vectors: no. Three vectors: yes.
Jarvis has written: 'Sequential constructions of orthonormal basis vectors, with statistical applications' -- subject(s): Regression analysis, Matrices, Vector analysis
No
Vectors that sum to zero are coplanar and coplanar vectors sum to zero.