A video lesson devoted to the rank of a matrix and its relationship with the linear independence of vectors.
In one of the examples, I show how to check the linear independence of vectors using the rank of a matrix.
I will show you the method I recommend for computing the rank of matrices, and you will see why computing rank by “zeroing” a row or column has a major advantage over the tedious search for proportional rows and columns.
You will also see what matrices and vectors have in common and what you actually gain from it.
Table of Contents
- Linear independence of vectors — definition [00:53]
- Rank of a matrix — definition (as the number of linearly independent rows/columns) [03:13]
- Computing the rank of matrices — Example 1 [05:09]
- Computing the rank of matrices — Example 2 [11:26]
- Computing the rank of matrices — Example 3 [14:43]
- Checking linear independence of vectors [20:28]
- Computing the rank of matrices — Example 4 [26:18]
