How to know the rank of a matrix with determinants

In this video I will explain how calculate the rank of a matrix with determinants.

The range will be equal to the number of linearly independent rows or columns.

We can calculate this, looking for your determinant.

1x1 matrix:

• If the determinant is different from zero, the range of A will be greater than or equal to one.
• If the determinant is not different from 0, the rank of A will be 0.

2x2 matrix:

• The matrix will have rank 2, if the determinant of the matrix is ​​not 0.
• If the determinant is 0, the range will be 1.

3x3 matrix:

• If the determinant is 0, the rank of A will be smaller than or equal to 2.

In the video you will see the practical verification of how to know the rank of a matrix with determinants. In addition, if you are not sure you can continue practicing with problems of this type you can do the printable exercises with their solutions that I have left you on the web. Good luck in your studies!

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