1 votes 1 votes Consider a matrix: $A =$ $\begin{bmatrix} 6 & 10\\ -2&-3 \end{bmatrix}$ The trace of $A^{10}$ is ______. Linear Algebra tbb-mockgate-3 numerical-answers engineering-mathematics linear-algebra eigen-value + – Bikram asked Feb 9, 2017 retagged Sep 16, 2020 by ajaysoni1924 Bikram 586 views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply Lucky sunda commented Feb 10, 2017 reply Follow Share Please explain. 1 votes 1 votes Bikram commented Feb 10, 2017 reply Follow Share see Trace of a Matrix https://en.wikipedia.org/wiki/Trace_(linear_algebra) 0 votes 0 votes Please log in or register to add a comment.
Best answer 7 votes 7 votes On solving - Eigen Values of A are 1 and 2. Thus eigen values of $A^{10}$ are $1^{10}$ and $2^{10} = 1$ and $1024$. We know trace of a matrix = sum of eigen values $= 1+1024 = 1025$ https://gatecse.in/wp-content/uploads/2015/07/evalue-magic-tricks-handout.pdf Harsh181996 answered Mar 13, 2017 selected Mar 13, 2017 by Bikram Harsh181996 comment Share Follow See all 2 Comments See all 2 2 Comments reply Satyajeet Singh commented Jan 16, 2018 reply Follow Share trace = sum of eign values above expression is valid for triangular matrix only rt?? 0 votes 0 votes Arjun commented Feb 1, 2018 reply Follow Share Nopes. It is for all $n \times n$ matrices. 1 votes 1 votes Please log in or register to add a comment.