Name the 10 Axioms from Chapter 4.1

(answer to this has ALL the answers. The following cards

will have fill in the blank)

1. If u and v are objects in V, then u + v is in V

2. u + v = v + u

3. u + (v+w) = (u+v) + w

4. There is an object 0 in V, called a zero vector for V, such that 0 + u = u + 0 = u for all u in V.

5. For each u in V, there is an object -u in V, called a negative of u, such that u + (-u) = (-u) + u = 0

6. if k is any scalar and u is any object in V, then ku is in V

7. k(u + v) = ku + kv

8. (k + m)u = ku + mu

9. k(mu) = (km)u

10. 1u = u

(Axioms related to 

a) 0u = 0

b) k0 = 0

c) (-1)u = -u

d) if ku = 0, then k = u or u = 0

if k is any scalar and u is any object in V, then _________

a) 0u = _

b) k0 = _

c) (-1)u = ___

d) if ku = 0, then ___________

a) 0u = 0

b) k0 = 0

c) (-1)u = -u

d) if ku = 0, then k = u or u = 0

4.8 Fundamental Matrix Spaces

If A is an n x n matrix, then the following statements are equivalent.

A is invertible?

a)      Ax = 0 ?

a)      The reduced row echelon form of A is ____

In

(identity matrix)

a)      A is expressible as a product of __________________

a)      Ax = b is consistent for every ________________

a)      Ax = b has exactly ______ solution for every n x 1 matrix b

a)      det(A) != ___

a)      The column vectors of A are linearly _______________

a)      The row vectors of A are linearly ______________

a)      The column vectors of A span _________

a)      The row vectors of A span ____

R^n

a)      The column vectors of A form a ______for R^n

a)      The row vectors of A form a _____for R^n

a)      A has rank ___

a)      A has nullity __

0

The orthogonal complement of the null space of A is ____

a)      The orthogonal complement of the row space of A is {0}

a)      The orthogonal complement of the row space of A is {0}