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 =3−15−3

Find the determinant det A of the matrix A shown.

A = [3 −1; 5 −3]
det A =
2.Easy
A =4−96−8

Find the determinant det A of the matrix A shown.

A = [4 −9; 6 −8]
det A =
3.Medium
A =0−323−444−3−2

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

A = [0 −3 2; 3 −4 4; 4 −3 −2]
det A =
4.Medium
A =−1−653B =041−4

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

A = [−1 −6; 5 3]B = [0 4; 1 −4]
c21 =
5.Hard
A =−6−643b =125

Solve the system −6x − 6y = 12 and 4x + 3y = 5. Find x.

−6x − 6y = 124x + 3y = 5
x =
6.Hard
A =4−4−14

Find the larger eigenvalue λ of the matrix A shown.

A = [4 −4; −1 4]
λ =

Answer key

  1. 1. det A = −4
  2. 2. det A = 22
  3. 3. det A = −52
  4. 4. c21 = 3
  5. 5. x = 11
  6. 6. λ = 6

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