0 votes 0 votes Linear Algebra eigen-value + – Hemanth_13 asked Jan 31, 2019 Hemanth_13 353 views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply newdreamz a1-z0 commented Jan 31, 2019 reply Follow Share (HERE X is the lambda) as eigen vaues are given the characteristic equation must be having factors 2,2,-1 so characteristic equation after solving | A-x*I |=0 will boil down to (x-2)*(x-2)*(x+1)=0 expand this equation and put x=A(as every matrix can be represented as it's eigen value lambda) 0 votes 0 votes aambazinga commented Jan 31, 2019 reply Follow Share A. (A+1)(A-2)$^{{2^{}}}$=0 Simplify the equation, multiply with A$^{-1}$, and put everything on RHS, except A$^{-1}$ on LHS. Answer will be A. 1 votes 1 votes Shaik Masthan commented Jan 31, 2019 reply Follow Share let check option by option, option A:- $P^{-1} = \frac{1}{4}(3P-P^2) $ $4.P^{-1} = (3P-P^2) $ multiply by P $4I = (3P^2-P^3) $ this is the characteristic eqn, so substitute $\lambda$ $\lambda=2$, then 4 = 12-8 ===> satisfies $\lambda=-1$, then 4 = 3-(-1) ===> satisfies so A is correct option ! 3 votes 3 votes Please log in or register to add a comment.