Across
- 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)
Down
- 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