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 =3−12−8

Find the determinant det A of the matrix A shown.

A = [3 −1; 2 −8]
det A =
2.Easy
A =1855

Find the determinant det A of the matrix A shown.

A = [1 8; 5 5]
det A =
3.Medium
A =13−35−500−50

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

A = [1 3 −3; 5 −5 0; 0 −5 0]
det A =
4.Medium
A =−3−6−15B =43−1−2

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

A = [−3 −6; −1 5]B = [4 3; −1 −2]
c12 =
5.Hard
A =5−4−51b =−38

Solve the system 5x − 4y = −3 and −5x + y = 8. Find x.

5x − 4y = −3−5x + y = 8
x =
6.Hard
A =63−8−4

Find the larger eigenvalue λ of the matrix A shown.

A = [6 3; −8 −4]
λ =

Answer key

  1. 1. det A = −22
  2. 2. det A = −35
  3. 3. det A = 75
  4. 4. c12 = 3
  5. 5. x = −1.933
  6. 6. λ = 2

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