Linear Algebra!

1. the identity matrix is ____
5. two matrices are ____ if one can be obtained from the other by a sequence of elementary row operations
8. an ____ of a n by n matrix A is a scalar c such that A*x = c*x holds for some nonzero vector x
9. the ____ of a vector space V is number of vectors in a basis for V
12. the ____ of vectors always forms a subspace
13. the solution set of the homogeneous equation Ax = 0
14. if A*B = B*A = I, B is the ____ of A
15. the ____ of a system with infinite number of solutions equals zero
17. the vectors are linearly ____ if the equation c₁u₁ + c₂u₂ +,..., cⁿuⁿ = 0 holds for some c ≠ 0
18. a finite set of vectors in a vector space that are linearly independent and span the vector space

1. a finite collection of vectors u₁, u₂,..., uⁿ in a vector space U whose span is U
2. the addition of scalar multiples of finitely many vectors
3. A system of linear equations A*x = b is ____ if b = 0
4. a convergent sequence is ____.
6. a nonempty subset of vector space that is closed under scalar multiplication and addition
7. a system of linear equations is ____ if it has at least one solution
10. the surname of one of your PASS leaders
11. the number of nonzero rows in any row equivalent matrix
16. the first non-zero entry in a row is the ____ entry