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 =13−75

Find the determinant det A of the matrix A shown.

A = [1 3; −7 5]
det A =
2.Easy
A =−9−76−9

Find the determinant det A of the matrix A shown.

A = [−9 −7; 6 −9]
det A =
3.Medium
A =44−1−4−2−54−5−3

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

A = [4 4 −1; −4 −2 −5; 4 −5 −3]
det A =
4.Medium
A =−3662B =−423−1

Let C = AB for the matrices shown. Find the entry c12 (row 1, column 2).

A = [−3 6; 6 2]B = [−4 2; 3 −1]
c12 =
5.Hard
A =3−15−3b =−8−9

Solve the system 3x − y = −8 and 5x − 3y = −9. Find x.

3x − y = −85x − 3y = −9
x =
6.Hard
A =1−4−52

Find the larger eigenvalue λ of the matrix A shown.

A = [1 −4; −5 2]
λ =

Answer key

  1. 1. det A = 26
  2. 2. det A = 123
  3. 3. det A = −232
  4. 4. c12 = −12
  5. 5. x = −3.75
  6. 6. λ = 6

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