Imagine two column vectors a1 and a2. both of these have 3 components, representing a point in 3d space
2a1 + a2 would be called a linear combination. many such linear combinations can be made. let's call that ca1 + da2
c and d are called scalars. they can be positive or negative. They could also be fractions or decimals
here's the starting idea of linear algebra: the combinations ca1 + da2 fill a plane inside 3d space - a flat sheet passing through the origin. every point on that plane is a combination of a1 and a2
not the whole of 3d space. just the sheet. you'd need a third vector pointing off it to reach everything else