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 =6−951

Find the determinant det A of the matrix A shown.

A = [6 −9; 5 1]
det A =
2.Easy
A =450−8

Find the determinant det A of the matrix A shown.

A = [4 5; 0 −8]
det A =
3.Medium
A =2−2−2434−1−45

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

A = [2 −2 −2; 4 3 4; −1 −4 5]
det A =
4.Medium
A =3265B =−1−40−5

Let C = AB for the matrices shown. Find the entry c21 (row 2, column 1).

A = [3 2; 6 5]B = [−1 −4; 0 −5]
c21 =
5.Hard
A =2634b =−1012

Solve the system 2x + 6y = −10 and 3x + 4y = 12. Find x.

2x + 6y = −103x + 4y = 12
x =
6.Hard
A =−1−379

Find the larger eigenvalue λ of the matrix A shown.

A = [−1 −3; 7 9]
λ =

Answer key

  1. 1. det A = 51
  2. 2. det A = −32
  3. 3. det A = 136
  4. 4. c21 = −6
  5. 5. x = 11.2
  6. 6. λ = 6

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