BIO1204 Lecture Notes - Lecture 5: Cravat, Free Variables And Bound Variables, If And Only If
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Example let a 32 9 find a basis for the eigenspace corresponding to eigenvalues x 1. 3. A a i n at basis for eigenvalue is t n a. m x the basis i. I 0 a at j 98 8. I 0 it 8 x the bass is it q. The columns are linearlydependent a is not invertible hence an eigenvalue. X a a by theorem 2 a has 3different eigenvectors. 1 v2. 4 and this is impossible since thevectorbelongs to two dimensional vector space in whichany set of. 3 vectors are linearly dependent if x is an eigenvalues of a then thereexist x such that axs xx since a is invertible. X aatx x o a is invertible thexoatxaacatxdatxatxsoaisaneigenvalueofaletaisthezeromatrixifaxsexforx0theaaxaxalalanazaaxazazsincex0andatothen120so70. A a it is invertible iff a ai is invertible. A a it is notinvertible iff a a1 isnotinvertible. That is x is eigenvalue ofa an eigenvalue of a tiff a is an informationwestudiedbeforebecauseif70thenadoandweknowthatxothenamustbeoanditwillbe2defanotinvertibleereesection 5. 2: the characteristic equation .
