Linear Algebra Crossword

7. two vectors are this if one can be changed to the other by a sequence of elementary row operations (2 words)
8. vectors are this if there is a nontrivial linear combination of the vectors that equals the zero vector (2 words)
9. Nonempty set of vectors closed under two operations and that is subject to ten axioms (2 words)
10. Word for if a matrix has a nonzero determinant
11. vector space generated by linear combinations of the matrix's row vectors (2 words)
12. matrix in which the entries outside the main diagonal are all zero
13. operations that allow one to transform a system of linear equations into an equivalent system (2 words)
16. Form a matrix can be in after Gaussian elimination (2 words)
18. The number of vectors in a basis for a vector space
20. Two or more equations that share variables (3 words)

1. Non-zero vector that can be changed at most by its scalar factor after the application of linear transformations
2. Scalar value that is a function of the entries of a square matrix
3. operator which flips a matrix over its diagonal
4. the span of a matrix's column vectors (2 words)
5. set of all linear combinations of a set of vectors
6. Function from one vector space to another that respects the underlying structure of each vector space (2 words)
14. a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros
15. the dimension of the vector space spanned by a matrix's columns
17. What two vectors are if their dot products is zero
19. Rectangular array of numbers, symbols, or expressions
21. Vector space that is a subset of some larger vector space