3 votes 3 votes How to solve this question? Linear Algebra linear-algebra eigen-value + – samarpita asked Dec 28, 2021 samarpita 577 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 5 votes 5 votes Eigen value of matrix X are -2 and -3 Eigen value of Identity matrix are 1 and 1 Now Eigen value for matrix $(X + I)^{-1}(X+5I)$ are = $(-2 + 1)^{-1}(-2+5)$ and $(-3 + 1)^{-1}(-3+5)$ = $-1*3$ and $\frac{-1}{2}*2$ = $-3$ and $-1$. Shoto answered Dec 28, 2021 selected Dec 29, 2021 by samarpita Shoto comment Share Follow See all 10 Comments See all 10 10 Comments reply Show 7 previous comments Shoto commented Dec 28, 2021 reply Follow Share src: https://www.geeksforgeeks.org/eigen-values-and-eigen-vectors/ 2 votes 2 votes ankitgupta.1729 commented Dec 29, 2021 reply Follow Share Nice answer. One thing might be mentioned that if matrix $A$ has Eigen value $\lambda$ and $B$ has Eigen value $\mu$ then matrix $AB$ has Eigen value $\lambda \mu$ if matrices $A,B$ and $AB$ share the same set of Eigen vectors..It can be proved easily...Here, matrices $(x+I)^{-1}$ and $(x+5I)$ always have the same set of Eigen vectors. Matrices $x,(x+I),(x+I)^{-1},(x+5I),(x+I)^{-1}(x+5I)$ all have the same set of Eigen vectors..This might be important because for similar kind of questions, there may give another matrix $B$ with Eigen value $\lambda$ and ask about the Eigen value $(x+I)^{-1}B$. 2 votes 2 votes samarpita commented Dec 29, 2021 reply Follow Share @ankitgupta.1729 yes my doubt is there only..I am asking him that only..same goes for addition also..that they must share common eigen vectors..then only we can add their eigen value 2 votes 2 votes Please log in or register to add a comment.