Test by Bikram | Mock GATE | Test 3 | Question: 54

Question

Consider a matrix:  

  $A =$ $\begin{bmatrix} 6 & 10\\ -2&-3 \end{bmatrix}$

 The trace of $A^{10}$ is ______.

Comments

Please explain.

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see Trace of a Matrix

https://en.wikipedia.org/wiki/Trace_(linear_algebra)

Answer 1

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

Comments

trace = sum of eign values

above expression  is valid for triangular matrix only rt??

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Nopes. It is for all $n \times n$ matrices.