Linear Algebra Practice Test
25 questions from 5 lessons · 75 minutes · percent score and grade · step-by-step answers
How it works
- 25 questions, about 75 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 0 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise these lessons next: the lessons of the questions you got wrong, with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
Formulas: the Linear Algebra formula sheet.
1 Question 1
Calculate (3, 1) + (2, 5)Type the answer.
2 Question 2
Calculate 3(1, 2, 0)Type the answer.
3 Question 3
Calculate 3(2, −1) + 2(1, 4)Type the answer.
4 Question 4
Calculate 2u + v for u = (3, −2), v = (−1, 5)Type the answer.
5 Question 5
Calculate 3(2, 1, −2) − 2(3, 0, −1) + (0, 4, 1)Type the answer.
6 Question 6
Rank of [1, 2; 2, 4]Type the answer.
7 Question 7
Rank of [1, 2, 3; 2, 4, 6]Type the answer.
8 Question 8
Rank of [1, 2, 1; 2, 4, 3; 3, 6, 4]Type the answer.
9 Question 9
Rank of [1, 3; 2, 6; −1, −3]Type the answer.
10 Question 10
Rank of [1, 2, 0, 1; 2, 4, 1, 4; 1, 2, 1, 3]Type the answer.
11 Question 11
Det by row operations [2, 1, 5; 0, 3, 4; 0, 0, −1]Type the answer.
12 Question 12
Det A = 6, find det(AT)Type the answer.
13 Question 13
Det by row operations [1, 2, 3; 0, 1, 4; 2, 5, 9]Type the answer.
14 Question 14
Det by row operations [3, 6, 3; 1, 4, 2; 2, 6, 7]Type the answer.
15 Question 15
Det A = −2, A is 3 × 3, find det(−A)Type the answer.
16 Question 16
Dot product of (1, 2, 3) and (4, −5, 6)Type the answer.
17 Question 17
Dot product of (1, −1, 2) and (2, 3, 1)Type the answer.
18 Question 18
Find the length of (1, 2, 2).Type the answer.
19 Question 19
Find the length of (2, 4, 2).Type the answer.
20 Question 20
Find the length of (1, −2, 3, 1).Type the answer.
21 Question 21
Least squares line through (−1, 2), (0, 1), (1, 6)Type the answer.
22 Question 22
Least squares line through (−1, 4), (0, 2), (1, 3)Type the answer.
23 Question 23
Least squares line through (0, 1), (1, 1), (2, 3)Type the answer.
24 Question 24
Least squares line through (−2, 1), (−1, 0), (0, 2), (1, 2), (2, 5)Type the answer.
25 Question 25
Least squares line through (−1, 0), (0, 1), (1, 1), (2, 4)Type the answer.