7 Linear Algebra IV

1. Given
   
   $$A = \left( \begin{array}{rrrr} -4 & -2 & 1 & 6 \\ 0 & 4 & -4 & 3 \\ 1 & 0 & 0 & 0 \end{array} \right)$$
   
   
   First find the rank, dimension of the row space, and dimension of the column space. Then find fully simplified bases of the row and column spaces.

2. Given
   
   $$A = \left( \begin{array}{rrrr} 4 & 3 & -5 & 6 \\ 1 & ... ... \\ 0 & -5 & 1 & 7 \\ 8 & 9 & 0 & 15 \end{array} \right)$$
   
   
   Find the determinant of this matrix both using minors and Gaussian elimination. Find the first row of the inverse matrix using minors.