Applied Mathematics 1411A/B Chapter 4.8.2: Applied Mathematics 1411A/B Chapter 4.8.: Applied Mathematics 1411A/B Chapter 4.8: Applied Mathematics 1411A/B Chapter 4.: Section 4.8.2
30 Dec 2018
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The following theorum established a fundamental relationship between the rank and the nullity of a matrix. If a is a matrix with n columns, then rank(a) + nullity(a) = n. If you want to find the rank and the nullity, you would have to follow the steps as we did before with reducing to rref to find rank. And equating the rref = 0 and solving for x in order to find the nullity. I guess in theory we don"t have to do both eh, we could find nullity by finding rank and then nullity(a) = n - rank(a). This next theorum interprets rank and nullity in the concept of a homogeneous linear system. Since a has n columns, the homogeneous linear system ax = 0 has n variables (x1, x2, , xn). This is because every column of a matrix corresponds to a variable.
