Etiqueta: Matrices

Ejercicios Propuestos

Ejercicios Propuestos – Determinante de una Matriz

Anthonny Arias García1 comentario

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

Proceda paso a paso, explicando detalladamente cada paso con sus propias palabras, la asignación correspondiente a su número de cédula.

Calcule el determinante de la matriz indicada.

1. \left( {\begin{array}{rr} -3 & 0 \\ 1 & 0 \\ \end{array} } \right)

2. \left( {\begin{array}{rr} 10 & 10 \\ 9 & -4 \\ \end{array} } \right)

3. \left( {\begin{array}{rr} -3 & -1 \\ 9 & 6 \\ \end{array} } \right)

4. \left( {\begin{array}{rr} 10 & -7 \\ -4 & 0 \\ \end{array} } \right)

5. \left( {\begin{array}{rr} -10 & -8 \\ -3 & 0 \\ \end{array} } \right)

6. \left( {\begin{array}{rr} -4 & 0 \\ 3 & 10 \\ \end{array} } \right)

7. \left( {\begin{array}{rr} 4 & 6 \\ 10 & -3 \\ \end{array} } \right)

8. \left( {\begin{array}{rr} 8 & 5 \\ 7 & 5 \\ \end{array} } \right)

9. \left( {\begin{array}{rrr} 2 & -2 & 4 \\ -7 & 0 & -6 \\ -2 & 8 & -8 \\ \end{array} } \right)

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

11. \left( {\begin{array}{rrr} 1 & 3 & -9 \\ -4 & 5 & -7 \\ 0 & -2 & 1 \\ \end{array} } \right)

12. \left( {\begin{array}{rrr} -8 & -2 & 9 \\ -5 & 0 & -1 \\ 9 & 5 & -7 \\ \end{array} } \right)

13. \left( {\begin{array}{rrr} 5 & -9 & 2 \\ 3 & 0 & -10 \\ 2 & 5 & -2 \\ \end{array} } \right)

14. \left( {\begin{array}{rrr} 0 & -9 & 9 \\ 10 & 10 & -2 \\ -10 & 6 & -8 \\ \end{array} } \right)

15. \left( {\begin{array}{rrr} 1 & 7 & -6 \\ 2 & -4 & -8 \\ 8 & 8 & 8 \\ \end{array} } \right)

16. \left( {\begin{array}{rrr} 5 & -4 & -10 \\ 8 & -2 & 0 \\ 8 & 5 & -5 \\ \end{array} } \right)

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Ejercicios Propuestos

Ejercicios Propuestos – Trasposición de matrices

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

Calcule la traspuesta de la matriz indicada.

1. \left( {\begin{array}{rr} 9 & -2 \\ \end{array} } \right)

2. \left( {\begin{array}{rr} 3 & 10 \\ \end{array} } \right)

3. \left( {\begin{array}{r} 7 \\ 6 \\ \end{array} } \right)

4. \left( {\begin{array}{r} -2 \\ 5 \\ \end{array} } \right)

5. \left( {\begin{array}{rrr} -7 & -4 & 1 \\ \end{array} } \right)

6. \left( {\begin{array}{rrr} 9 & -5 & -9 \\ \end{array} } \right)

7. \left( {\begin{array}{r} -9 \\ 3 \\ 10 \\ \end{array} } \right)

8. \left( {\begin{array}{r} 8 \\ 8 \\ -9 \\ \end{array} } \right)

9. \left( {\begin{array}{rr} 3 & -7 \\ -5 & -3 \\ \end{array} } \right)

10. \left( {\begin{array}{rr} -1 & 10 \\ 1 & -1 \\ \end{array} } \right)

11. \left( {\begin{array}{rr} 2 & -9 \\ 8 & 6 \\ 2 & -7 \\ \end{array} } \right)

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

13. \left( {\begin{array}{rrr} 7 & -3 & -9 \\ -1 & 9 & 2 \\ \end{array} } \right)

14. \left( {\begin{array}{rrr} -9 & 1 & -10 \\ 3 & -2 & 5 \\ \end{array} } \right)

15. \left( {\begin{array}{rrr} 9 & -1 & 3 \\ -2 & -9 & -9 \\ 5 & 8 & -1 \\ \end{array} } \right)

16. \left( {\begin{array}{rrr} -3 & -3 & -1 \\ 4 & -7 & 8 \\ 4 & 8 & 9 \\ \end{array} } \right)

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Ejercicios Propuestos

Ejercicios Propuestos – Producto de una matriz por un escalar

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

Calcule el producto de la matriz por el escalar indicado.

1. 6 \cdot \left( {\begin{array}{rr} 10 & -7 \\ \end{array} } \right)

2. 9 \cdot \left( {\begin{array}{rr} 1 & -5 \\ \end{array} } \right)

3. 9 \cdot \left( {\begin{array}{r} -1 \\ -3 \\ \end{array} } \right)

4. 2 \cdot \left( {\begin{array}{r} -6 \\ 4 \\ \end{array} } \right)

5. -6 \cdot \left( {\begin{array}{rrr} 9 & -7 & -8 \\ \end{array} } \right)

6. -1 \cdot \left( {\begin{array}{rrr} -8 & -1 & 1 \\ \end{array} } \right)

7. -4 \cdot \left( {\begin{array}{r} -7 \\ -7 \\ 7 \\ \end{array} } \right)

8. -4 \cdot \left( {\begin{array}{r} 7 \\ -7 \\ 7 \\ \end{array} } \right)

9. 7 \cdot \left( {\begin{array}{rr} -3 & -8 \\ -3 & 9 \\ \end{array} } \right)

10. 9 \cdot \left( {\begin{array}{rr} -7 & -2 \\ 7 & 10 \\ \end{array} } \right)

11. 7 \cdot \left( {\begin{array}{rr} -2 & -5 \\ 10 & -1 \\ 7 & -7 \\ \end{array} } \right)

12. -5 \cdot \left( {\begin{array}{rr} -2 & 5 \\ -5 & -10 \\ 6 & -5 \\ \end{array} } \right)

13. 2 \cdot \left( {\begin{array}{rrr} -5 & -10 & -3 \\ 1 & -5 & 7 \\ \end{array} } \right)

14. 10 \cdot \left( {\begin{array}{rrr} 4 & -10 & -1 \\ 5 & -4 & -5 \\ \end{array} } \right)

15. 10 \cdot \left( {\begin{array}{rrr} -10 & 6 & -2 \\ 10 & -8 & 3 \\ -10 & 2 & 5 \\ \end{array} } \right)

16. -4 \cdot \left( {\begin{array}{rrr} -10 & 7 & 2 \\ 7 & -7 & -1 \\ -3 & -7 & 8 \\ \end{array} } \right)

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Ejercicios Propuestos

Ejercicios Propuestos – Producto de Matrices

Anthonny Arias GarcíaDeja un comentario
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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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Ejercicios Propuestos

Ejercicios Propuestos – Resta de Matrices

Anthonny Arias GarcíaDeja un comentario

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

1. \left( {\begin{array}{rr} -3 & 10 \\ \end{array} } \right) - \left( {\begin{array}{rr} -5 & 4 \\ \end{array} } \right)

2. \left( {\begin{array}{rr} -1 & -10 \\ \end{array} } \right) - \left( {\begin{array}{rr} -2 & -9 \\ \end{array} } \right)

3. \left( {\begin{array}{rr} 3 & -9 \\ \end{array} } \right) - \left( {\begin{array}{rr} 10 & -9 \\ \end{array} } \right)

4. \left( {\begin{array}{rr} -4 & 7 \\ \end{array} } \right) - \left( {\begin{array}{rr} 4 & 10 \\ \end{array} } \right)

5. \left( {\begin{array}{r} 1 \\ -5 \\ \end{array} } \right) - \left( {\begin{array}{r} 9 \\ 5 \\ \end{array} } \right)

6. \left( {\begin{array}{r} -5 \\ -4 \\ \end{array} } \right) - \left( {\begin{array}{r} 2 \\ -3 \\ \end{array} } \right)

7. \left( {\begin{array}{r} 2 \\ -8 \\ \end{array} } \right) - \left( {\begin{array}{r} -7 \\ 1 \\ \end{array} } \right)

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

9. \left( {\begin{array}{rrr} -2 & -10 & -2 \\ \end{array} } \right) - \left( {\begin{array}{rrr} -5 & -3 & -10 \\ \end{array} } \right)

10. \left( {\begin{array}{rrr} -5 & 1 & 8 \\ \end{array} } \right) - \left( {\begin{array}{rrr} 6 & -10 & -8 \\ \end{array} } \right)

11. \left( {\begin{array}{rrr} 6 & 5 & -7 \\ \end{array} } \right) - \left( {\begin{array}{rrr} 4 & -3 & -2 \\ \end{array} } \right)

12. \left( {\begin{array}{rrr} -5 & -4 & -7 \\ \end{array} } \right) - \left( {\begin{array}{rrr} 2 & 2 & -3 \\ \end{array} } \right)

13. \left( {\begin{array}{r} -2 \\ 1 \\ 2 \\ \end{array} } \right) - \left( {\begin{array}{r} 8 \\ -6 \\ 4 \\ \end{array} } \right)

14. \left( {\begin{array}{r} -5 \\ 2 \\ -1 \\ \end{array} } \right) - \left( {\begin{array}{r} 8 \\ 8 \\ 4 \\ \end{array} } \right)

15. \left( {\begin{array}{r} 3 \\ 2 \\ 6 \\ \end{array} } \right) - \left( {\begin{array}{r} 5 \\ 2 \\ 9 \\ \end{array} } \right)

16. \left( {\begin{array}{r} -10 \\ 4 \\ -5 \\ \end{array} } \right) - \left( {\begin{array}{r} -2 \\ -8 \\ -4 \\ \end{array} } \right)

17. \left( {\begin{array}{rr} -7 & 1 \\ -9 & -8 \\ \end{array} } \right) - \left( {\begin{array}{rr} -5 & 2 \\ 7 & 7 \\ \end{array} } \right)

18. \left( {\begin{array}{rr} 9 & 3 \\ -5 & 2 \\ \end{array} } \right) - \left( {\begin{array}{rr} -7 & -2 \\ -3 & -9 \\ \end{array} } \right)

19. \left( {\begin{array}{rr} 2 & 3 \\ 7 & -5 \\ \end{array} } \right) - \left( {\begin{array}{rr} 5 & 9 \\ -8 & -8 \\ \end{array} } \right)

20. \left( {\begin{array}{rr} 8 & 8 \\ 5 & -9 \\ \end{array} } \right) - \left( {\begin{array}{rr} -6 & -5 \\ -10 & 2 \\ \end{array} } \right)

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

22. \left( {\begin{array}{rr} -3 & 8 \\ 2 & 5 \\ 2 & -7 \\ \end{array} } \right) - \left( {\begin{array}{rr} 1 & -3 \\ 10 & 8 \\ -9 & 5 \\ \end{array} } \right)

23. \left( {\begin{array}{rr} -5 & 6 \\ -5 & -10 \\ -10 & -5 \\ \end{array} } \right) - \left( {\begin{array}{rr} 9 & 4 \\ 5 & 8 \\ -5 & 4 \\ \end{array} } \right)

24. \left( {\begin{array}{rr} 7 & -10 \\ -9 & 7 \\ -9 & -7 \\ \end{array} } \right) - \left( {\begin{array}{rr} -4 & -3 \\ -10 & 7 \\ 10 & -1 \\ \end{array} } \right)

25. \left( {\begin{array}{rrr} 5 & 10 & 4 \\ -7 & -4 & 10 \\ \end{array} } \right) - \left( {\begin{array}{rrr} -2 & -6 & -2 \\ -6 & 2 & -10 \\ \end{array} } \right)

26. \left( {\begin{array}{rrr} 5 & -3 & -10 \\ -8 & -4 & 2 \\ \end{array} } \right) - \left( {\begin{array}{rrr} -9 & 10 & -5 \\ 8 & 7 & -8 \\ \end{array} } \right)

27. \left( {\begin{array}{rrr} -9 & -1 & 1 \\ 7 & 7 & 9 \\ \end{array} } \right) - \left( {\begin{array}{rrr} 10 & -9 & -8 \\ -2 & 9 & 4 \\ \end{array} } \right)

28. \left( {\begin{array}{rrr} -8 & 1 & 1 \\ -9 & 4 & -5 \\ \end{array} } \right) - \left( {\begin{array}{rrr} 8 & -6 & -1 \\ -5 & -5 & 8 \\ \end{array} } \right)

29. \left( {\begin{array}{rrr} 3 & 6 & -6 \\ 5 & -8 & -6 \\ 10 & -9 & -6 \\ \end{array} } \right) - \left( {\begin{array}{rrr} 8 & -10 & -3 \\ 5 & -3 & -2 \\ 4 & -9 & -7 \\ \end{array} } \right)

30. \left( {\begin{array}{rrr} -4 & 7 & 1 \\ -3 & 8 & -3 \\ 2 & -6 & -1 \\ \end{array} } \right) - \left( {\begin{array}{rrr} -6 & -8 & -10 \\ -6 & 4 & 8 \\ 5 & 8 & 9 \\ \end{array} } \right)

31. \left( {\begin{array}{rrr} -10 & 9 & 3 \\ -8 & 6 & 9 \\ -10 & -4 & -1 \\ \end{array} } \right) - \left( {\begin{array}{rrr} 7 & 7 & 3 \\ -1 & -3 & -9 \\ -3 & -1 & 5 \\ \end{array} } \right)

32. \left( {\begin{array}{rrr} 8 & 6 & -6 \\ 9 & 3 & -3 \\ 1 & -3 & -3 \\ \end{array} } \right) - \left( {\begin{array}{rrr} -7 & -1 & 10 \\ -7 & -8 & -6 \\ 3 & 1 & -3 \\ \end{array} } \right)

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