[beginarrayll2&15&3endarray]

Frequently Asked Questions

• Evaluate the determinant of $\left[\begin{array}{ll}2& 1\\ 5& 3\end{array}\right]$

  

  $$1$$

• Find the matrix inverse of $\left[\begin{array}{ll}2& 1\\ 5& 3\end{array}\right]$

  

  $$\left[\begin{array}{ll}3& -1\\ -5& 2\end{array}\right]$$

• Find the matrix transpose of $\left[\begin{array}{ll}2& 1\\ 5& 3\end{array}\right]$

  

  $$\left[\begin{array}{ll}2& 5\\ 1& 3\end{array}\right]$$

• Find the eigenvalues of $\left[\begin{array}{ll}2& 1\\ 5& 3\end{array}\right]$

  

  $${\lambda }_1=\frac{5-\sqrt{21}}{2},{\lambda }_2=\frac{5+\sqrt{21}}{2}$$

• Find the row echelon form of $\left[\begin{array}{ll}2& 1\\ 5& 3\end{array}\right]$

  

  $$\left[\begin{array}{ll}2& 1\\ 0& \frac{1}{2}\end{array}\right]$$

• Find the reduced row echelon form of $\left[\begin{array}{ll}2& 1\\ 5& 3\end{array}\right]$

  

  $$\left[\begin{array}{ll}1& 0\\ 0& 1\end{array}\right]$$