91Ó°ÊÓ

Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). $$\left[\begin{array}{ll}1 & 2 \\\3 & 4\end{array}\right]$$

$$\text { Do }\left[\begin{array}{l} 1 \\ 1 \\ 0 \end{array}\right],\left[\begin{array}{l} 0 \\ 1 \\ 1 \end{array}\right],\left[\begin{array}{l} 1 \\ 0 \\ 1 \end{array}\right] \text { form a basis for } \bar{Z}_{2}^{3}?$$

Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). $$\left[\begin{array}{rr}-2 & 4 \\\3 & -1\end{array}\right]$$

Draw a graph that has the given adjacency matrix. $$\left[\begin{array}{lllll} 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 1 & 1 \\ 1 & 0 & 0 & 0 & 1 \\ 1 & 1 & 0 & 0 & 0 \\ 0 & 1 & 1 & 0 & 0 \end{array}\right]$$

Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). $$\left[\begin{array}{rr}3 & -4 \\\\-6 & 8\end{array}\right]$$

Draw a graph that has the given adjacency matrix. $$\left[\begin{array}{lllll} 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 & 1 \\ 1 & 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 \end{array}\right]$$

Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). $$\left[\begin{array}{rr}1 & a \\\\-a & 1\end{array}\right]$$

Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). $$\left[\begin{array}{rrr}2 & 0 & -1 \\\1 & 5 & 1 \\\2 & 3 & 0\end{array}\right]$$

Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists). $$\left[\begin{array}{rrr}1 & -1 & 2 \\\3 & 1 & 2 \\\2 & 3 & -1\end{array}\right]$$

Compute the rank and nullity of the given matrices over the indicated \(\mathbb{Z}_{p}\)? $$\left[\begin{array}{lll} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \end{array}\right] \text { over } \mathbb{Z}_{2}$$