Based vector

When a vector v is considered as an arrow from the origin to a point p, we say v is based

Linear combination of a single vector

scalar multiple of v

Linear equation

An algebraic equation where each term is either a constant or the product of a constant and a single variable raised to the first power

What is R^n?

R^n is just the set of all (ordered) lists of n real numbers.

Span

Vector equation

A vector equation is an equation involving a linear combination of vectors with possibly unknown coefficients.

How can you know whether a vector equation has a solution?

Check if a given vector is a linear combination of some other given vectors???????????????????????????????????????????????????????????????? 9sstraight from textbook this class makes NO SENSE3

Consistent system

If one or more solutions exist for an equation or a system of equations

Inconsistent system

If an equation or system of equations does not have any solution

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