Hi there!

I was wondering if there is a list of facts showing what makes a linearly independent and linearly dependent matrix?

For example, if there is a 3x3 matrix with a row of zeros, does that make the matrix linearly dependent?

For example, how is this matrix linearly independent?

[16 1]

[1 17]

[0 0]

[0 0]

Doesn't this have a row of zeros, so it should be dependent?

the matrix:

[1 3 -5]

[5 2 7]

[0 0 0]

Is linearly dependent because it has a row of zeros.