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 =4−649

Find the determinant det A of the matrix A shown.

A = [4 −6; 4 9]
det A =
2.Easy
A =−4282

Find the determinant det A of the matrix A shown.

A = [−4 2; 8 2]
det A =
3.Medium
A =−43−2−3B =0−2−61

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

A = [−4 3; −2 −3]B = [0 −2; −6 1]
c22 =
4.Medium
A =3−2−135−4032

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

A = [3 −2 −1; 3 5 −4; 0 3 2]
det A =
5.Hard
A =−4−454b =−60

Solve the system −4x − 4y = −6 and 5x + 4y = 0. Find x.

−4x − 4y = −65x + 4y = 0
x =
6.Hard
A =1−2−54

Find the larger eigenvalue λ of the matrix A shown.

A = [1 −2; −5 4]
λ =

Answer key

  1. 1. det A = 60
  2. 2. det A = −24
  3. 3. c22 = 1
  4. 4. det A = 69
  5. 5. x = −6
  6. 6. λ = 6

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