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 =5540

Find the determinant det A of the matrix A shown.

A = [5 5; 4 0]
det A =
2.Easy
A =−2−3−5−5

Find the determinant det A of the matrix A shown.

A = [−2 −3; −5 −5]
det A =
3.Medium
A =−3−5442−5100

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

A = [−3 −5 4; 4 2 −5; 1 0 0]
det A =
4.Medium
A =012−3B =−2−356

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

A = [0 1; 2 −3]B = [−2 −3; 5 6]
c21 =
5.Hard
A =6642b =−108

Solve the system 6x + 6y = −10 and 4x + 2y = 8. Find x.

6x + 6y = −104x + 2y = 8
x =
6.Hard
A =−1−3−24

Find the larger eigenvalue λ of the matrix A shown.

A = [−1 −3; −2 4]
λ =

Answer key

  1. 1. det A = −20
  2. 2. det A = −5
  3. 3. det A = 17
  4. 4. c21 = −19
  5. 5. x = 5.667
  6. 6. λ = 5

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