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 =−4−13−5

Find the determinant det A of the matrix A shown.

A = [−4 −1; 3 −5]
det A =
2.Easy
A =−7−55−9

Find the determinant det A of the matrix A shown.

A = [−7 −5; 5 −9]
det A =
3.Medium
A =−3531−3−54−3−1

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

A = [−3 5 3; 1 −3 −5; 4 −3 −1]
det A =
4.Medium
A =−315−5B =−3532

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

A = [−3 1; 5 −5]B = [−3 5; 3 2]
c21 =
5.Hard
A =02−57

Find the larger eigenvalue λ of the matrix A shown.

A = [0 2; −5 7]
λ =
6.Hard
A =4614b =−5−10

Solve the system 4x + 6y = −5 and x + 4y = −10. Find x.

4x + 6y = −5x + 4y = −10
x =

Answer key

  1. 1. det A = 23
  2. 2. det A = 88
  3. 3. det A = −32
  4. 4. c21 = −30
  5. 5. λ = 5
  6. 6. x = 4

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