What is the rank of a given matrix?

[g.lemaitre]

Homework Statement

find rk(A) for the following matrix

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

Homework Equations

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.

 

[Robert1986]

Homework Statement

find rk(A) for the following matrix

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

Homework Equations

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.

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.

 

[g.lemaitre]

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

 

[Robert1986]

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

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

 

[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.

 

[g.lemaitre]

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

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