Worksheet 4

1. Use Gaussian Elimination to determine if the following matrix is invertible. If so, determine the inverse. \(\begin{pmatrix} 1 & 0 & 1 \\ 1 & -1 & 1 \\ 0 & 1 & 1 \end{pmatrix}\)

2. Use Gaussian Elimination to determine if the following matrix is invertible. If so, determine the inverse. \(\begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix}\)

3. Determine which the following statements are true and which are false:

   • If a matrix is invertible, it has to be diagonal.
   • Diagonal matrices are invertible.
   • If $A$ has a zero column, it is not invertible.