Matrices & determinants worksheet with answers

Free printable Matrices & determinants worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
A =−5−10−9

Find the determinant det A of the matrix A shown.

A = [−5 −1; 0 −9]
det A =
2.Easy
A =−27−4−7

Find the determinant det A of the matrix A shown.

A = [−2 7; −4 −7]
det A =
3.Medium
A =−1−4−4−3B =33−43

Let C = AB for the matrices shown. Find the entry c22 (row 2, column 2).

A = [−1 −4; −4 −3]B = [3 3; −4 3]
c22 =
4.Medium
A =−404−4−4−243−5

Find the determinant det A of the 3×3 matrix A shown.

A = [−4 0 4; −4 −4 −2; 4 3 −5]
det A =
5.Hard
A =0−156

Find the larger eigenvalue λ of the matrix A shown.

A = [0 −1; 5 6]
λ =
6.Hard
A =34−63b =−73

Solve the system 3x + 4y = −7 and −6x + 3y = 3. Find x.

3x + 4y = −7−6x + 3y = 3
x =

Answer key

  1. 1. det A = 45
  2. 2. det A = 42
  3. 3. c22 = −21
  4. 4. det A = −88
  5. 5. λ = 5
  6. 6. x = −1

Full step-by-step solutions: practise this topic on examproblems.com.