- #1

- 818

- 8

**I don't understand why the rank = n -- Rank-nullity theorem -- nullity**

## Homework Statement

I'm working on #1 (the solutions are also included in that pdf) here ( http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/ax-b-and-the-four-subspaces/exam-1/MIT18_06SCF11_ex1s.pdf ).

## Homework Equations

A

**x**=

**b**

A

**x**=

**0**

rank A+ nullity A = n

## The Attempt at a Solution

For #1(a), I don't understand why the rank = n. I've been told to look at the Rank-nullity theorem which states that rank A+ nullity A = n but, I don't understand what nullity means exactly. In fact, I'm not very solid on the meaning of rank either (but, I kind of get it).

Any input would be greatly appreciated!