**1.** Create the matrix $$\text{matA}=\begin{pmatrix} 3&5&2\\7&-3&8\\2&-4&1\end{pmatrix}$$

**2. **Find the determinant

**3.** Find the inverse

**4.** Find the transpose

**5.** Find the eigenvalues and eigenvectors for the matrix: $\begin{pmatrix} 1&4\\3&2\end{pmatrix}$

The output is in the form (**eigenvalue**, **eigenvector**, **multiplicity**). In this example, for eigenvalue $\lambda_1=5$ we have $v_1=\begin{pmatrix}1\\\frac{4}{3}\end{pmatrix}$ with multiplicity 1, and for $\lambda_2=-2$, $v_2=\begin{pmatrix}1\\-1\end{pmatrix}$, also with multiplicity of 1. A slightly better output might be:

**6.** For the system of equations: $\left\{\begin{align}-2x+3y&=13\\5x-2y&=6\end{align}\right.$, use the inverse matrix to solve the matrix equation $A\textbf{x}=B$.

There is also a command in Sage, **.solve_right()**, that will solve this equation:

Checking the solution: