Linear Algebra Practice Test

Name: ______________________   Date: __________   Score: ____ / 25

25 questions. Calculator allowed. Show your working. steplyclass.com/linear-algebra/practice-test/

1. 1

   Calculate (3, 1) + (2, 5)

   Answer: ____________________

2. 2

   Calculate 3(1, 2, 0)

   Answer: ____________________

3. 3

   Calculate 3(2, −1) + 2(1, 4)

   Answer: ____________________

4. 4

   Calculate 2u + v for u = (3, −2), v = (−1, 5)

   Answer: ____________________

5. 5

   Calculate 3(2, 1, −2) − 2(3, 0, −1) + (0, 4, 1)

   Answer: ____________________

6. 6

   Rank of [1, 2; 2, 4]

   Answer: ____________________

7. 7

   Rank of [1, 2, 3; 2, 4, 6]

   Answer: ____________________

8. 8

   Rank of [1, 2, 1; 2, 4, 3; 3, 6, 4]

   Answer: ____________________

9. 9

   Rank of [1, 3; 2, 6; −1, −3]

   Answer: ____________________

10. 10

    Rank of [1, 2, 0, 1; 2, 4, 1, 4; 1, 2, 1, 3]

    Answer: ____________________

11. 11

    Det by row operations [2, 1, 5; 0, 3, 4; 0, 0, −1]

    Answer: ____________________

12. 12

    Det A = 6, find det(A^T)

    Answer: ____________________

13. 13

    Det by row operations [1, 2, 3; 0, 1, 4; 2, 5, 9]

    Answer: ____________________

14. 14

    Det by row operations [3, 6, 3; 1, 4, 2; 2, 6, 7]

    Answer: ____________________

15. 15

    Det A = −2, A is 3 × 3, find det(−A)

    Answer: ____________________

16. 16

    Dot product of (1, 2, 3) and (4, −5, 6)

    Answer: ____________________

17. 17

    Dot product of (1, −1, 2) and (2, 3, 1)

    Answer: ____________________

18. 18

    Find the length of (1, 2, 2).

    Answer: ____________________

19. 19

    Find the length of (2, 4, 2).

    Answer: ____________________

20. 20

    Find the length of (1, −2, 3, 1).

    Answer: ____________________

21. 21

    Least squares line through (−1, 2), (0, 1), (1, 6)

    Answer: ____________________

22. 22

    Least squares line through (−1, 4), (0, 2), (1, 3)

    Answer: ____________________

23. 23

    Least squares line through (0, 1), (1, 1), (2, 3)

    Answer: ____________________

24. 24

    Least squares line through (−2, 1), (−1, 0), (0, 2), (1, 2), (2, 5)

    Answer: ____________________

25. 25

    Least squares line through (−1, 0), (0, 1), (1, 1), (2, 4)

    Answer: ____________________