CHAPTER 10.09: EIGENVALUES AND
EIGENVECTORS: Theorems of eigenvalues and eigenvectors Part 2 of 6 In
this segment we will talk about some theorems of eigenvalues and eigenvectors
so the second theorem right here saying that if λ=0 is an eigenvalue of
a nxn [A] matrix, then [A] is noninvertible so if
you find out that one of the eigenvalues of the [A] matrix of a square matrix
turns out to be zero just one then the [A] matrix is noninvertible which is
the same as saying (singular) which is the same as saying its inverse doesn’t
exist and so on and so forth so that’s what it is telling you so for example
if somebody says that hey this is my matrix given to me [A]=5, 6, 2, 3, 5, 9,
2, 1, -7 for this particular matrix if you go through the process of finding
the eigenvalues you will find that λ=0 is an eigenvalue youll find one of the eigenvalues is zero so what does
that mean that means that [A] inverse does not exist that means that A inverse does not exist or it means that [A] is not
invertible it means [A] is singular it also means that the det(A)=0 because if A inverse
does not exist then we know that for a square matrix the det
of that matrix has to be equal to zero that’s the end of this segment |