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 =−12−3−8

Find the determinant det A of the matrix A shown.

A = [−1 2; −3 −8]
det A =
2.Easy
A =−3223

Find the determinant det A of the matrix A shown.

A = [−3 2; 2 3]
det A =
3.Medium
A =−6−5−3−1B =3−30−4

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

A = [−6 −5; −3 −1]B = [3 −3; 0 −4]
c12 =
4.Medium
A =−2−2−6−1B =3−4−52

Let C = AB for the matrices shown. Find the entry c22 (row 2, column 2).

A = [−2 −2; −6 −1]B = [3 −4; −5 2]
c22 =
5.Hard
A =4−11−4b =6−1

Solve the system 4x − y = 6 and x − 4y = −1. Find x.

4x − y = 6x − 4y = −1
x =
6.Hard
A =2−136

Find the larger eigenvalue λ of the matrix A shown.

A = [2 −1; 3 6]
λ =

Answer key

  1. 1. det A = 14
  2. 2. det A = −13
  3. 3. c12 = 38
  4. 4. c22 = 22
  5. 5. x = 1.667
  6. 6. λ = 5

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