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 =3−6−16

Find the determinant det A of the matrix A shown.

A = [3 −6; −1 6]
det A =
2.Easy
A =−262−7

Find the determinant det A of the matrix A shown.

A = [−2 6; 2 −7]
det A =
3.Medium
A =1−3−3−524−1−2−1

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

A = [1 −3 −3; −5 2 4; −1 −2 −1]
det A =
4.Medium
A =2−320B =3−416

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

A = [2 −3; 2 0]B = [3 −4; 1 6]
c12 =
5.Hard
A =−32−87

Find the larger eigenvalue λ of the matrix A shown.

A = [−3 2; −8 7]
λ =
6.Hard
A =−3−643b =4−5

Solve the system −3x − 6y = 4 and 4x + 3y = −5. Find x.

−3x − 6y = 44x + 3y = −5
x =

Answer key

  1. 1. det A = 12
  2. 2. det A = 2
  3. 3. det A = −3
  4. 4. c12 = −26
  5. 5. λ = 5
  6. 6. x = −1.2

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