PreCalculus – Chapter 8 Test Review – Matrix Algebra All questions worth 1 point unless otherwise stated. Total 29 points.

Perform the following computations. 1. [ 2.

] [

[

[

]

] [

]

3. [

][

]

[

[

]

] ]

[ 4. [

][

5. [

[

]

]

] [

]

6. If AB = BA what do you know about matrices A and B?

]

They are inverses of each other.

7. What are two reasons why some matrices don’t have inverses? The determinant could be zero, or they might not be square. Find the determinants and inverses of the following matrices. 8. [

(2 points each)

]

8 [

9. [

[

]

]

Many elementary row operations that will require extra paper

]

[

[

]

]

156+192+192 208+192+144 544-540 Solve the following systems. (

10.

[

11.

[

]

]

[

]

[

[

]

]

)

(

[

)

][

1 ***3 possible extra credit points : do #9, 11 by hand. You can use a calculator to check.***

]

Review. Switch between polar form (trigonometric form) and rectangular form (a+bi form). ( ) √( ) 12. √ (

)

13.

)

√(

14. (

)

( )

(

√

√

)

15. (

)

√

√

Simplify. 16. 17.

18. ( (

)) ( √ (

19. ( (

))

20. ( (

))

21. √ (

√ (

))

( √ (

√

))

) or √

(

)

(

)

(2 points)

√ (

√

)

√

√

√

)

22. √ √ (

)

√ (

(2 points)

√

√

√

√

√

)

Find the angle between the vectors. 23. 〈 24. 〈

〉〈

〉 〉〈

√

〉

25. Find a vector orthogonal to 〈

√

√

√

〉

answers can vary

〈

〉 or 〈

〉