Linear Algebra Vocabulary

2. A vector space within another vector space.
5. A matrix where the left-most value in a row is 1, or the whole row consists of zeros is in _____ _____ _____ form.
6. A _____ matrix has the same number of rows as columns.
9. A system where one of its vectors is a multiple of another vector.
10. The _____ of a matrix is when the rows and columns of a matrix get swapped.
13. A space where ten axioms of vector addition and scalar multiplication are satisfied.
15. A value that has both magnitude and direction.

1. A matrix has an inverse when it is ______.
3. A value obtained in square matrices that can be used to find the inverse of a system of equations or solve it.
4. The number of vectors in a vector space.
7. The _____ of a matrix is the transpose of the cofactor matrix.
8. A system that always has the trivial solution.
11. A matrix that has a pivot in all its non-zero rows is in ______ _____ form.
12. P is a _____ of V when it spans V and is linearly independent.
14. The set S _____ set V when every vector in V can be created from a linear combination of the vectors in S.