I and J are the basis vectors of a coordinate system and thus in this section of the course, any vector can be denoted as a linear combination of A(I) + B(J).
The set of all possible vectors that you can reach with a linear combination of a given pair of vectors is the span of those vectors. For example, a span of 2 vectors would be a sheet cutting through the origin unless if the 2 vectors were part of a single line.
Then what is the span of a 3 dimensional vector?
1 case is that the 3rd vector lies on the span of the first two vectors thus not impacting the span of the total sum of vectors. We call the third vector, a linearly dependant vector as it can be represented as a linear combination of the other 2 vectors.
Conversely, a vector in a different direction would provide access to the whole 3d space and this vector would be known as being linearly dependent.
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