Ejercicios Propuestos – Producto de Matrices

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Proceda paso a paso, explicando detalladamente cada paso con sus propias palabras.

Calcule el producto entre matrices indicado y su conmutación, ¿los resultados son iguales? En caso de no poder efectuar el producto, indique porqué.

1. $\left( {\begin{array}{r} 5 \\ 5 \\ -5 \\ \end{array} } \right) \times \left( {\begin{array}{rr} 6 & -1 \\ -6 & -3 \\ 2 & 3 \\ \end{array} } \right)$

2. $\left( {\begin{array}{rrr} -1 & 5 & -6 \\ 4 & -8 & 9 \\ -7 & -1 & 7 \\ \end{array} } \right) \times \left( {\begin{array}{rr} -4 & 8 \\ 10 & -5 \\ -10 & 7 \\ \end{array} } \right)$

3. $\left( {\begin{array}{r} -3 \\ -3 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} -1 & 5 & 3 \\ \end{array} } \right)$

4. $\left( {\begin{array}{rrr} 9 & -10 & -4 \\ \end{array} } \right) \times \left( {\begin{array}{r} -8 \\ 7 \\ -3 \\ \end{array} } \right)$

5. $\left( {\begin{array}{rr} -9 & -7 \\ -6 & 1 \\ \end{array} } \right) \times \left( {\begin{array}{rr} -4 & -10 \\ -7 & 9 \\ \end{array} } \right)$

6. $\left( {\begin{array}{r} 3 \\ -6 \\ \end{array} } \right) \times \left( {\begin{array}{rr} -10 & -5 \\ 10 & -4 \\ \end{array} } \right)$

7. $\left( {\begin{array}{r} -2 \\ 3 \\ -3 \\ \end{array} } \right) \times \left( {\begin{array}{r} 9 \\ -6 \\ 7 \\ \end{array} } \right)$

8. $\left( {\begin{array}{rrr} 5 & -10 & -3 \\ 10 & -4 & -2 \\ \end{array} } \right) \times \left( {\begin{array}{r} -7 \\ 10 \\ \end{array} } \right)$

9. $\left( {\begin{array}{rr} 9 & -8 \\ \end{array} } \right) \times \left( {\begin{array}{rr} -8 & -7 \\ \end{array} } \right)$

10. $\left( {\begin{array}{rrr} 8 & 7 & 8 \\ -4 & -8 & 3 \\ \end{array} } \right) \times \left( {\begin{array}{rr} -2 & -7 \\ -7 & -2 \\ -8 & 10 \\ \end{array} } \right)$

11. $\left( {\begin{array}{rr} -9 & 1 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 3 & -4 & 3 \\ -7 & 2 & -2 \\ 6 & -8 & 2 \\ \end{array} } \right)$

12. $\left( {\begin{array}{rrr} -1 & -8 & 9 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} -6 & 2 & 8 \\ \end{array} } \right)$

13. $\left( {\begin{array}{rr} 1 & -9 \\ -10 & -8 \\ -1 & 8 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 1 & -9 & 10 \\ -9 & -6 & 4 \\ \end{array} } \right)$

14. $\left( {\begin{array}{rrr} -4 & -9 & 10 \\ 9 & 2 & -9 \\ \end{array} } \right) \times \left( {\begin{array}{rr} 4 & -3 \\ 8 & -5 \\ \end{array} } \right)$

15. $\left( {\begin{array}{rrr} 7 & 3 & -6 \\ -3 & 5 & -2 \\ 7 & -1 & -8 \\ \end{array} } \right) \times \left( {\begin{array}{r} 4 \\ 2 \\ -10 \\ \end{array} } \right)$

16. $\left( {\begin{array}{rrr} -5 & -2 & 7 \\ 5 & -3 & 2 \\ -4 & -7 & 4 \\ \end{array} } \right) \times \left( {\begin{array}{r} 8 \\ -5 \\ \end{array} } \right)$

17. $\left( {\begin{array}{rr} 3 & -7 \\ 7 & -3 \\ 7 & 1 \\ \end{array} } \right) \times \left( {\begin{array}{r} -6 \\ -6 \\ \end{array} } \right)$

18. $\left( {\begin{array}{rr} 4 & 1 \\ 1 & -10 \\ -3 & 8 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 5 & -3 & -2 \\ 2 & -3 & -5 \\ 3 & -3 & 1 \\ \end{array} } \right)$

19. $\left( {\begin{array}{r} -9 \\ 4 \\ 4 \\ \end{array} } \right) \times \left( {\begin{array}{r} 8 \\ -5 \\ -1 \\ \end{array} } \right)$

20. $\left( {\begin{array}{rrr} 7 & 10 & -9 \\ 1 & 5 & 6 \\ -4 & -2 & 8 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 6 & 8 & -9 \\ \end{array} } \right)$

21. $\left( {\begin{array}{rr} -6 & -1 \\ -10 & -8 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} -6 & 1 & 6 \\ -1 & -7 & 5 \\ -6 & -6 & -9 \\ \end{array} } \right)$

22. $\left( {\begin{array}{rr} -2 & 5 \\ -3 & 10 \\ -8 & 3 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 3 & 3 & -8 \\ 9 & -9 & 6 \\ \end{array} } \right)$

23. $\left( {\begin{array}{r} 8 \\ -7 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} -1 & -5 & -9 \\ 9 & 10 & 7 \\ \end{array} } \right)$

24. $\left( {\begin{array}{rrr} -10 & 10 & 6 \\ \end{array} } \right) \times \left( {\begin{array}{rr} 7 & 3 \\ 3 & 10 \\ -2 & -5 \\ \end{array} } \right)$

25. $\left( {\begin{array}{rrr} 9 & 1 & -4 \\ 2 & -5 & -9 \\ 7 & 8 & -3 \\ \end{array} } \right) \times \left( {\begin{array}{rr} -8 & 7 \\ -3 & -1 \\ \end{array} } \right)$

26. $\left( {\begin{array}{r} 1 \\ -1 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 6 & -8 & -4 \\ \end{array} } \right)$

27. $\left( {\begin{array}{rrr} -9 & -2 & -10 \\ -3 & -1 & -5 \\ -8 & 5 & 9 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} -9 & 3 & -7 \\ \end{array} } \right)$

28. $\left( {\begin{array}{rrr} 7 & -7 & 3 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 5 & -4 & 5 \\ \end{array} } \right)$

29. $\left( {\begin{array}{rr} 3 & 10 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 8 & 5 & 7 \\ -1 & -4 & -2 \\ -3 & -5 & 4 \\ \end{array} } \right)$

30. $\left( {\begin{array}{rr} 6 & -8 \\ -2 & -7 \\ -10 & 8 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} 8 & -5 & 5 \\ \end{array} } \right)$

31. $\left( {\begin{array}{rr} 4 & 7 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} -2 & 7 & -6 \\ 9 & 7 & -7 \\ \end{array} } \right)$

32. $\left( {\begin{array}{r} -1 \\ -2 \\ \end{array} } \right) \times \left( {\begin{array}{rrr} -6 & -3 & 8 \\ \end{array} } \right)$

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