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


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