Linear Algebra

(eigenvector)

*Please answer all parts.

1 ~l E 11. LetA: -l 1 2 ' 2 -2 ll 1 {i paints.) Show that "1 is an aim of A. What. is the Eigenvalue? 2 .3 iJ {ii} {5 painter.) What" :5 the ran]; of A? Ebrp]3.i.1:-l {briey} why this makes {II an aiganvnlue 91' A with multiplicity 2 ' ' l.- {iii} {5 paints} Find El-bask far the gimme for tha aigenwlue 11 {iv} {5 paints} Find an ntthugnnal basis fez-r R\" HIBiEIIE of eiganvacmra Elf A. You My haw: u. :igmucctam