Revision Flashcards
What is rank A
number of pivots of A
dim Col A
dim Row A
What is Row A
set of all linear combinations of rows of A
Col A^T
What is Nul A
Set of all solutions Ax=0
Span {solution}
What is Col A
set all linear combinations of columns of A
Span{a1, a2, …, an}
What is the Kernel of a transformation
set of all u : T(u)=0
What is dim Nul A
number of free variables in Ax=0
What is dim Col A
number of pivot columns in A
How
b contained in span of columns of A
[A b] consistent
What is basis Col A
formed by the original columns with a pivot in it
What is basis Nul A
formed by solution of Ax=0
When is A invertible
det A /=0
How can you find y2 in Ay=b
y2 = (det A2(b))/det A
How to prove T is a linear transformation
T(u+v) = T(u) + T(v) T(cu) = c T(u)
How to prove H is a subspace
contains zero vector
contains u+v
contains cu
How to prove T is one-to-one
A has pivot in every column
How to prove T is onto
A has pivot in every row
What is range T?
range T = Col A
What is basis range T
basis Col A
What is dim Ker T
dim Nul A
When are the columns of A linearly independent
A has a pivot in every column
What is basis Row A
set of row vectors with pivots
When is A a basis for Rn
when A has a pivot in every row and column
det B-1 = 1 / det B
