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Let each matrix in Exercises $1-6$ act on $\mathbb{C}^{2} .$ Find the eigenvalues and a basis for each eigenspace in $\mathbb{C}^{2} .$$$\left[\begin{array}{rr}{4} & {3} \\ {-3} & {4}\end{array}\right]$$

$\mathbf { v } _ { 2 } = \overline { \mathbf { v } _ { 1 } } = \left[ \begin{array} { l } { i } \\ { 1 } \end{array} \right]$

Calculus 3

Chapter 5

Eigenvalues and Eigenvectors

Section 5

Complex Eigenvalues

Vectors

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Okay, so for problem six give the matrix is 43 negative. Three and four. So consider determined off a mine. Islam die. This will be for minus I three. Next week, three, four minutes. I he's here now. By solving the you question, you find out London should be for plus or minus three. I okay, And to find out basis we first take London to before Waas three. I I'm sorry and this difference would be negative. Three i and three and neck of three and thank you. Three I now by I really applying the culture and damnation get the reduce station form. So the result would be I active one 00 So if we flooding our unknown vector excuse me are unknown vectored to be ex lax too. Then by the first roll we have on times X one minus x two will be zero. Now that is I time sex one would be x two. So our first base is will be one Excuse me, one and I And our second business will be one and negative. Hi. So

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