Mathematics, 18.08.2020 14:01 okokjade
Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C².
[1 3]
[-3 1]
Answers: 1
such that A
![A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}](/tpl/images/0723/7859/e3278.png)
![A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}](/tpl/images/0723/7859/79a29.png)
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Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C².
[1 3]
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