Linear Algebra Test 1 - TFAE
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3
A has n pivot positions
1
A is invertible
2
A is row equivalent to In
8
A spans Rn
12
AT is invertible
4
Ax=0 has only the trivial solution
7
Ax=b has a solution for each b in Rn
5
The columns of A are linearly independent
10
There is an n X n matrix C such that CA=I
11
There is an n X n matrix D such that AD=I
6
x |-> Ax is 1-to-1
9
x |-> Ax maps Rn onto Rn
