Definitions Flashcards
1
Q
Elementary matrix
A
A matrix obtained by performing a single elementary row operation on an identity matrix
2
Q
Subspace
A
Any set H in Rn that has these three properties:
a) The zero vector is in H
b) For each u and v in H u+v is in H
c) For each u in H and each scalar in c, the vector cu is in H.
3
Q
Column space
A
The of set all linear combinations of the columns of matrix A
4
Q
Null space`
A
The of all solutions of the homogenous equation Ax =0 in matrix A
5
Q
Basis
A
A linearly independent set in H that spans H
6
Q
Dimension
A
A nonzero subspace H, denoted by dim H, is the number of vectors in any basis for H. The dimensiom of the zero subspace{0} is defined to be zero
7
Q
Rank
A
The dimension of the column space of A. Rank = num pivot columns
