1 1 vote Let $A$ be a $3\times 3$ matrix with Eigen values $-1,1,0$.Then $\mid A^{100}+I\mid$ is... Linear Algebra engineering-mathematics linear-algebra eigen-value + – Avik Chowdhury 1.0k views answer comment Share Follow Print See 1 comment 1 1 comment reply V Y commented Mar 22, 2018 reply Follow flag Eigen value of A (-1,1,0) given. So, the eigen value of A^100 will be [ (-1)^100 , (1)^100, (0)^100 which is (1,1,0) ] hence the Eigen value of matrix --> [ A^100+ I ] = ( 1+1 , 1+1 ,0+1 ) = (2,2,1) . As it is asking for |A^100+I| = Product of it's Eigen value = ( 2*2*1 ) = 4 . 4 4 replyShare Please log in or register to add a comment.
1 1 vote EIGEN VALUES OF A^(100) will be (-1)^(100)=1 (1)^(100) =1 , (0)^(100)=0, det|A^(100)+ I| = 2*2*1 =4 Kaluti answered Mar 29, 2018 Kaluti comment Share Follow 0 reply Please log in or register to add a comment.
