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.

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1.Easy
A =2−8−99

Find the determinant det A of the matrix A shown.

A = [2 −8; −9 9]
det A =
2.Easy
A =−4−4−5−4

Find the determinant det A of the matrix A shown.

A = [−4 −4; −5 −4]
det A =
3.Medium
A =5−312−234−5−1

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

A = [5 −3 1; 2 −2 3; 4 −5 −1]
det A =
4.Medium
A =6−32−4B =−5314

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

A = [6 −3; 2 −4]B = [−5 3; 1 4]
c12 =
5.Hard
A =−36−1−2b =101

Solve the system −3x + 6y = 10 and −x − 2y = 1. Find x.

−3x + 6y = 10−x − 2y = 1
x =
6.Hard
A =2112

Find the larger eigenvalue λ of the matrix A shown.

A = [2 1; 1 2]
λ =

Answer key

  1. 1. det A = −54
  2. 2. det A = −4
  3. 3. det A = 41
  4. 4. c12 = 6
  5. 5. x = −2.167
  6. 6. λ = 3

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