1. Let and . Find the eigenvalues of this matrix and determine if it is invertible. In other wo...

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1. Let $TE L(V)$ and $0 0 8$ . Find the eigenvalues of this matrix and determine if it is invertible. In other words, how does finding a basis of $V$ for which the matrix of $T$ is upper triangular help find the eigenvalues of $T$ and how does it help determine is $T$ is invertible?

2. Define $T\in L(\mathbb{F}^3)$ by $T(x_{1},x_{2},x_{3})=(4x_{3},-3x_{2},0)$ . Find all the eigenvalues and eigenvectors of $T$ . Note $\mathbb{F}$ stands for either $\mathbb{R}$ or $\mathbb{C}$ .

TE L(V)
0 0 8

math Advanced-Math

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ILu vWest Bengal s-> 3 08 λ=2, 5, 8 . Mrn 2.5, g 80 3 ntu αλ SCHoUl auuCaiu Ly 3レ 33レ etrn

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