[ ( a 11 −λ ) a 12 ⋯ a 1n a 21 ( a 22 −λ ) ⋯ a 2n ⋮ a n 1 ⋮ a n2 ⋮ ⋯ ( a nn −λ ) ] . [ x 1 x 2 ⋮ x n ] = [ 0 0 ⋮ 0 ] |A−λI | = | ( a 11 − λ ) a 12 ⋯ a 1 n a 21 ( a 22 −λ ) ⋯ a 2 n ⋮ a n 1 ⋮ a n 2 ⋯ ⋮ ( a nn −λ ) | =0 A = [ 2 0 1 −1 4 −1 −1 2 0 ] | ( 2− λ ) 0 1 − 1 ( 4−λ ) − 1 − 1 2 −λ | =0 ( 2− λ ) { − λ ( 4−λ ) +2 }+1 { −2 +( 4−λ ) }=0 ( 2− λ ) {λ 2 −4 λ +2 }+( 2− λ )= 0 ( 2− λ ) {λ 2 −4 λ +3 } = 0 λ =1,2,3. A = [ 2 1 1 1 3 2 −1 1 2 ]
