Lahat na

Vector Addition

u + v, u + v, u + v,…,u + v

Scalar multiplication

ku, ku, … , ku

Difference of 2 vectors

v - u, v - u, … , v - u

Euclidean Norm

Euclidean Distance

Dot Product

Unit vector

Angle between 2 vectors

Linear Independent

Is true when 𝑐1 = 𝑐2 = ⋯ = 𝑐𝑛 = 0, meaning if all solutions are only zero

Linear Dependent

When the solution to fhe equation can be a nonzero value

S spans V

If the linear system is consistent without any restriction on the arbitrary vector 𝛼,

S does not span V

If the linear system is to be consistent only by imposing some conditions on 𝛼

Cofactor

Inverse of A

Adjoint of matrix A

obtained by replacing the entries of 𝐴 by their corresponding cofactors,

Parallel Vectors

u • v = ||u|| ||v||

Orthogonal Vectors

cos φ = 0