Suppose you want to know the eigenvalues of the following matrix:

$$A=\left(\begin{array}{cc}-2& -24\\ 3& 16\end{array}\right)$$

1. Create a new document and select Add Calculator.
2. Create the matrix:
   • Press and select Matrix & Vector > Create > Matrix.
   • Enter the number of rows (2) and columns (2). Press and write the matrix values.
3. Store the matrix and name it a: Press and . Write a and press .
4. Compute the eigenvalues:
   • Press and select Matrix & Vector > Advanced > Eigenvalues.
   • Write a inside the brackets of eigVl() and press .

   

   The results should be ${\lambda }_1=4$ and ${\lambda }_2=10$, which are the eigenvalues.

Consider the following matrix:

$$A=\left(\begin{array}{cc}-2& -24\\ 3& 16\end{array}\right)$$

Suppose you want to compute the eigenvectors associated with ${\lambda }_1=4$ and ${\lambda }_2=10$.

1. Write the homogeneous linear system associated with the eigenvalue: $$(A-\lambda I)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}0\\ 0\end{array}\right)$$ Here: $$\{\begin{array}{l}-6x-24y=0\\ 3x+12y=0\end{array}$$
2. Solve the system using the calculator:
   • Press and select Algebra > Solve System of Equations > Solve System of Linear Equations.
   • The result should display $y$ as a free variable and $x=-4y$.

   

3. Interpret the solution:

   The eigenvectors are represented as: $$t\left(\begin{array}{c}-4\\ 1\end{array}\right)$$ Here, $t$ is a free variable. A possible eigenvector is: $$x_1=\left(\begin{array}{c}-4\\ 1\end{array}\right)$$

4. Repeat the process for ${\lambda }_2=10$. A possible eigenvector is: $$x_2=\left(\begin{array}{c}-2\\ 1\end{array}\right)$$