1. $5\times 4;9$

2. $\left[\begin{array}{rrrr}7& -3& 9& 5\\ -2& 4& 3& -12\\ 8& -5& 1& -9\end{array}\right]$

3. $\{\begin{array}{rrrrrrr}4x& -& & & z& =& -3\\ x& +& 3y& & & =& 9\\ 2x& +& 7y& +& 5z& =& 8\end{array}$

4. (10, 10, 0)

5. $\{(2,3,-2)\}$

6. $\left\{({\displaystyle \frac{20}{7}}+{\displaystyle \frac{11}{7}}z,{\displaystyle \frac{2}{7}}+{\displaystyle \frac{6}{7}}z,z)\right\}$

7. $A-B=\left[\begin{array}{rr}8& -1\\ 4& 8\\ 11& 0\end{array}\right]$

8. $AB=[1]$

9. The product AB is not defined.

10. $\left[\begin{array}{rrr}-6& 2& 0\\ 10& 14& 4\end{array}\right]$

11. $\left[\begin{array}{rrr}20& 28& 8\\ -9& 29& 6\end{array}\right]$

12. $\left[\begin{array}{ll}1& 25\\ 0& 26\end{array}\right]$

13. $\left[\begin{array}{rr}1& -{\displaystyle \frac{5}{4}}\\ 0& {\displaystyle \frac{1}{4}}\end{array}\right]$

14. $\left[\begin{array}{rrr}-11& 2& 7\\ 8& -1& -5\\ 5& -1& -3\end{array}\right]$

15. $\left[\begin{array}{rr}5& 2\\ 3& 1\end{array}\right]\left[\begin{array}{l}x\\ y\end{array}\right]=\left[\begin{array}{l}32\\ 18\end{array}\right]$

16. $\{\begin{array}{lllll}12x& -& 3y& =& 5\\ -2x& +& 7y& =& -9\end{array}$

17. $X=\left[\begin{array}{rrr}-{\displaystyle \frac{3}{5}}& -1& 4\\ -{\displaystyle \frac{32}{5}}& -{\displaystyle \frac{18}{5}}& -3\end{array}\right]$

18. ${\displaystyle \frac{1}{2}}$

19. 0

20. $x={\displaystyle \frac{\left|\begin{array}{rrr}3& -1& 1\\ 6& 1& 1\\ 4& 3& -2\end{array}\right|}{\left|\begin{array}{rrr}2& -1& 1\\ 1& 1& 1\\ 4& 3& -2\end{array}\right|}},y={\displaystyle \frac{\left|\begin{array}{rrr}2& 3& 1\\ 1& 6& 1\\ 4& 4& -2\end{array}\right|}{\left|\begin{array}{rrr}2& -1& 1\\ 1& 1& 1\\ 4& 3& -2\end{array}\right|}},$

$z={\displaystyle \frac{\left|\begin{array}{rrr}2& -1& 3\\ 1& 1& 6\\ 4& 3& 4\end{array}\right|}{\left|\begin{array}{rrr}2& -1& 1\\ 1& 1& 1\\ 4& 3& -2\end{array}\right|}}$