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 =5−835

Find the determinant det A of the matrix A shown.

A = [5 −8; 3 5]
det A =
2.Easy
A =8−65−3

Find the determinant det A of the matrix A shown.

A = [8 −6; 5 −3]
det A =
3.Medium
A =−52−5121−2−13

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

A = [−5 2 −5; 1 2 1; −2 −1 3]
det A =
4.Medium
A =50−24B =40−5−3

Let C = AB for the matrices shown. Find the entry c11 (row 1, column 1).

A = [5 0; −2 4]B = [4 0; −5 −3]
c11 =
5.Hard
A =131−3b =7−4

Solve the system x + 3y = 7 and x − 3y = −4. Find x.

x + 3y = 7x − 3y = −4
x =
6.Hard
A =0−299

Find the larger eigenvalue λ of the matrix A shown.

A = [0 −2; 9 9]
λ =

Answer key

  1. 1. det A = 49
  2. 2. det A = 6
  3. 3. det A = −60
  4. 4. c11 = 20
  5. 5. x = 1.5
  6. 6. λ = 6

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