Linear Algebra - find rk(A)

1. Jul 19, 2012

g.lemaitre

1. The problem statement, all variables and given/known data

find rk(A) for the following matrix

[3 -6]
[5 -10]
[-2 4]

2. Relevant equations
3. The attempt at a solution

How am I supposed to find the answer when I don't know what r is? I thought r had to be a number or a scalar and you multiply the whole matrix by it.

2. Jul 19, 2012

Robert1986

rk(A) is the rank of A, which is the dimension of the image of the matrix, or, equivalently, the number of linearly independent columns in the matrix.

3. Jul 19, 2012

g.lemaitre

ok, got it, but you can easily see how that could throw one off when given the following theorem:

4. Jul 19, 2012

Robert1986

Not really. Didn't your book define rk(A)? The theorem was about dot products.

5. Jul 19, 2012

Muphrid

A point that might help here as far as notation goes: usually, functions like sine, cosine, and rank are written in fully upright, non-italic, non-bold letters, e.g. $\sin \theta$ or $\text{rk}(A)$. Scalar variables, on the other hand, will usually be italicized. $rk$ is the product of the variables $r$ and $k$.

6. Jul 19, 2012

g.lemaitre

When you're coming across new notation it's easy to get them confused.