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 =4−95−9

Find the determinant det A of the matrix A shown.

A = [4 −9; 5 −9]
det A =
2.Easy
A =037−3

Find the determinant det A of the matrix A shown.

A = [0 3; 7 −3]
det A =
3.Medium
A =−55−104−1−30−1

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

A = [−5 5 −1; 0 4 −1; −3 0 −1]
det A =
4.Medium
A =−3455B =−1−4−24

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

A = [−3 4; 5 5]B = [−1 −4; −2 4]
c12 =
5.Hard
A =0−4−62

Find the larger eigenvalue λ of the matrix A shown.

A = [0 −4; −6 2]
λ =
6.Hard
A =4−43−1b =−10−10

Solve the system 4x − 4y = −10 and 3x − y = −10. Find x.

4x − 4y = −103x − y = −10
x =

Answer key

  1. 1. det A = 9
  2. 2. det A = −21
  3. 3. det A = 23
  4. 4. c12 = 28
  5. 5. λ = 6
  6. 6. x = −3.75

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