MATH 152

Angle Between 2 Vectors

Dot Product of Two Perpendicular Vectors

0

Dot Product of Two Parallel Vectors

1

Projection of V onto W

Linear Independence

RREF Matrix has no free variables

There is no non-trivial combination of the vectors

Determinate of vectors does not equal 0

All 0s in the last row except the law column

No Solution

No free variables

Unique Solution

There is at least one free variable

Infinite Solution

Rank is equal to the amount of vectors

unique solution

Rank is less than the amount of vectors

infinite solution

Homogeneous Systems

All 0s on the right hand side of a RREF and there is at least one solution.