Suppose that n ≥ 2 and let T = [tij] ∈ Mn be upper triangular. Explain why en is an eigenvector

Name: Suppose that n ≥ 2 and let T = [tij] ∈ Mn be upper triangular. Explain why en is an eigenvector associated with eigenvalue tnn.
Uploaded: 2023-01-12T19:02:56-08:00
Duration: 2 min 3 s
Channel: Diogo Caetano
Description: Suppose that n ≥ 2 and let T = [tij] ∈ Mn be upper triangular. Explain why en is an eigenvector associated with eigenvalue tnn.

Question

Diogo Caetano · Accepted Answer

Step 1: 
An upper triangular matrix T has the form:
[ T = begin{bmatrix}
t_{11} & t_{12} & t_{13

Question

Suppose that $n \ge 2$ and let $T = [t_{ij}] \in M_n$ be upper triangular. Explain why $e_n$ is an eigenvector associated with eigenvalue $t_{nn}$.

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