Linear Algebra with Applications, 10th Edition

2.2

1. 1. 

   1. (a) $-24$;

   2. (b) 30;

   3. (c) $-1$

2. 2. 

   1. (a) 10;

   2. (b) 20

3. 3. (a), (e), and (f) are singular while (b), (c), and (d) are nonsingular.

4. 4. $c=5\text{ or }-3$

5. 5. Hint: What is the effect on det(A) if you multiply just one row of A by α? When you do the scalar multiplication αA you are multiplying all of the rows of A by α.

6. 6. Hint: Use Theorem2.2.3 to prove the result.

7. 7. 

   1. (a) 20;

   2. (b) 108;

   3. (c) 160;

   4. (d) $\frac{5}{4}$

8. 9. 

   1. (a) $-6$;

   2. (c) 6;

   3. (e) 1

9. 10. Hint: Look at the list of important concepts for this section.

10. 11. Hint: Show that if A is a n × n whose entries are real numbers then $\det \left(A^2\right)\ge 0.$

11. 12. 

    1. (a) Hint: Use elimination to zero out the (2,1) and (3,1) entries of V before computing its determinant.

12. 13. $\text{det}(A)=u_{11}{u}_{22}{u}_{33}$

13. 14. Hint: Use Theorem2.2.3 .

14. 15. Hint: If ...