# Find the characteristic polynomial of the matrices begin{bmatrix}2 & 1 -1 & 3 end{bmatrix}

Find the characteristic polynomial of the matrices
$\left[\begin{array}{cc}2& 1\\ -1& 3\end{array}\right]$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Ezra Herbert
Step 1 we have to find the characteristic polynomial of the matrices
$A=\left[\begin{array}{cc}2& 1\\ -1& 3\end{array}\right]$
Step 2
$A=\left[\begin{array}{cc}2& 1\\ -1& 3\end{array}\right]$
for characteristic polynomial:
$|A-\lambda I|=\left[\begin{array}{cc}2-\lambda & 1\\ -1& 3-\lambda \end{array}\right]$
$=\left(2-\lambda \right)\left(3-\lambda \right)-\left(-1\right)\left(1\right)$
$=\left(2-\lambda \right)\left(3-\lambda \right)+1$
$=2\left(2-\lambda \right)-\lambda \left(3-\lambda \right)+1$
$=6-2\lambda -3\lambda +{\lambda }^{2}+1$
$={\lambda }^{2}-5\lambda +7$
the characteristic polynomial is $f\left(\lambda \right)={\lambda }^{2}-5\lambda +7$
Jeffrey Jordon