Linear combination and span
Last updated
Last updated
A linear combination of the vectors x, y and z is any vector of the form a x + b y + c z where a, b and c are constants.
Example: (8,3,3) is a linear combination of (1,1,1) and (1,0,0) since it satisfies the following equation with constants 3 and 5.
The linear span of the vectors x and y is the set of all possible linear combinations of them.
Example: The linear span of (1,1,1) and (1,0,0) is the set of all vectors of the form
where s and t range over all possible scalar values.
Link: http://faculty.bard.edu/belk/math213s14/LinearCombinationsAndSpanRevised.pdf