What Does 'Combination' Mean in a Linear Algebra Context?

[kolycholy]

i am a bit confused
what does it mean when somebody says "all combinations of (1, 2, 3, 0) and (2, 3, 4, 0)"??

 

[TD]

I suspect they mean all lineair combinations, i.e. a*(1,2,3,0)+b*(2,3,4,0), with a,b scalars.

 

[tacman]

In a linear algebra context, a combination refers to a linear combination, which is a mathematical operation that involves multiplying each element in a set of vectors by a constant and then adding them together. In other words, it is a linear combination of vectors if it can be expressed as a linear combination of those vectors.

In the given example, "all combinations of (1, 2, 3, 0) and (2, 3, 4, 0)" means that any vector that can be obtained by multiplying (1, 2, 3, 0) and (2, 3, 4, 0) by constants and adding them together is considered a combination. So, for instance, (5, 8, 11, 0) would be a combination of (1, 2, 3, 0) and (2, 3, 4, 0) since it can be expressed as 5(1, 2, 3, 0) + 3(2, 3, 4, 0).

I hope this clarifies the concept of combination in a linear algebra context.