# Shared Flashcard Set

Linear Algreba
Study
31
Mathematics
04/16/2012

## Additional Mathematics Flashcards

Term
 Name the 10 Axioms from Chapter 4.1 (answer to this has ALL the answers. The following cards will have fill in the blank)
Definition
 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
Term
 If u and v are objects in V, then ________
Definition
 u + v is in V
Term
 u + v = _______
Definition
 v + u
Term
 u + (v+w) = __________
Definition
 (u+v) + w
Term
 There is an object 0 in V, called a zero vector for V, such that ________________________________
Definition
 0 + u = u + 0 = u for all u in V.
Term
 For each u in V, there is an object -u in V, called a negative of u, such that _______________________
Definition
 u + (-u) = (-u) + u = 0
Term
 if k is any scalar and u is any object in V, then _________
Definition
 ku is in V
Term
 k(u + v) = ______________
Definition
 ku + kv
Term
 (k + m)u = ___________
Definition
 ku + mu
Term
 k(mu) = ________
Definition
 (km)u
Term
 1u = __
Definition
 u
Term
 a) 0u = _ b) k0 = _ c) (-1)u = ___ d) if ku = 0, then ___________
Definition
 a) 0u = 0 b) k0 = 0 c) (-1)u = -u d) if ku = 0, then k = u or u = 0
Term
 4.8 Fundamental Matrix Spaces If A is an n x n matrix, then the following statements are equivalent.
Definition
Term
 A is invertible?
Definition
 Yes
Term
 a)      Ax = 0 ?
Definition
 Yes
Term
 a)      The reduced row echelon form of A is ____
Definition
 In (identity matrix)
Term
 a)      A is expressible as a product of __________________
Definition
 elementary matrices
Term
 a)      Ax = b is consistent for every ________________
Definition
 n x 1 matrix b
Term
 a)      Ax = b has exactly ______ solution for every n x 1 matrix b
Definition
 one
Term
 a)      det(A) != ___
Definition
 0
Term
 a)      The column vectors of A are linearly _______________
Definition
 independent
Term
 a)      The row vectors of A are linearly ______________
Definition
 independent.
Term
 a)      The column vectors of A span _________
Definition
 R^n
Term
 a)      The row vectors of A span ____
Definition
 R^n
Term
 a)      The column vectors of A form a ______for R^n
Definition
 basis
Term
 a)      The row vectors of A form a _____for R^n
Definition
 basis
Term
 a)      A has rank ___
Definition
 n
Term
 a)      A has nullity __
Definition
 0
Term
 The orthogonal complement of the null space of A is ____
Definition
 R^n
Term
 a)      The orthogonal complement of the row space of A is {0}
Definition
 a)      The orthogonal complement of the row space of A is {0}
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