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5 Answers

Best answer
47 votes
47 votes

The Eigen values for upper triangular/lower triangular/diagonal matrices are the diagonal elements of the matrix.

$\therefore$ The Eigen values are $1,2,-2,-1.$

edited by
18 votes
18 votes
$A=\begin{bmatrix} 1& 2 &34 &49\\ 0& 2&43 &94\\ 0& 0 & -2&104\\ 0& 0& 0&-1 \end{bmatrix}$

$|A-\lambda I |=0$

$\begin{vmatrix} 1-\lambda& 2 &34 &49\\ 0& 2-\lambda&43 &94\\ 0& 0 & -2-\lambda&104\\ 0& 0& 0&-1-\lambda \end{vmatrix}=0$

$( 1-\lambda)( 2-\lambda)( -2-\lambda)(-1-\lambda)=0$

$\lambda=1\ ,\ -1\ ,\ 2 \ , \ -2$
1 votes
1 votes
Eigen value $lambda$=1,-1,2,-2 A-$lambda$I=0 just solve it and for the 2nd question i think building a truth table is a naive way of answering it if any1 has better solution then plz reply
0 votes
0 votes
if the matrix is either upper triangular or lower triangular matrix then the principal diagonal element are called eigen value.
1,2,-1,-2 for this question ...

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