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 =1923

Find the determinant det A of the matrix A shown.

A = [1 9; 2 3]
det A =
2.Easy
A =6462

Find the determinant det A of the matrix A shown.

A = [6 4; 6 2]
det A =
3.Medium
A =411−41−1−113

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

A = [4 1 1; −4 1 −1; −1 1 3]
det A =
4.Medium
A =535−4B =3543

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

A = [5 3; 5 −4]B = [3 5; 4 3]
c12 =
5.Hard
A =−524−1b =3−6

Solve the system −5x + 2y = 3 and 4x − y = −6. Find x.

−5x + 2y = 34x − y = −6
x =
6.Hard
A =−1421

Find the larger eigenvalue λ of the matrix A shown.

A = [−1 4; 2 1]
λ =

Answer key

  1. 1. det A = −15
  2. 2. det A = −12
  3. 3. det A = 26
  4. 4. c12 = 34
  5. 5. x = −3
  6. 6. λ = 3

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